Some Applications of Trigonometry

1. Heights and Distances

MCQ

1. If a pole 6 m high casts a shadow 2 √ 3 m long on the ground, then sun's elevation is
(2023)
(a) 60° (b) 45° (c) 30° (d) 90°
2. A ladder makes an angle of 60° with the ground when placed against a wall. If the foot of the
ladder is 2 m away from the wall, then the length of the ladder (in meters) is (Delhi 2014)
4
(a) √ 3 (b) 4 3√ (c) 2 √ 2 (d) 4
3. The angle of depression of a car parked on the road from the top of a 150 m high tower is
30°. The distance of the car from the tower (in metres) is (Al 2014) Ap

(a) 50 √3 (b) 150 √3 (c) 150√ 2 (d) 75

4. If the height of a vertical pole is √ 3 times the length of its shadow on the ground, then the
angle of elevation of the Sun at that time is (Foreign 2014)
(a) 30° (b) 60° (c) 45° (d) 75°
VSA (1 mark)
5. In figure, the angle of elevation of the top of a tower from a point C on the ground, which is
30 m away from the foot of the tower, is 30°. Find the height of the tower. (2020) Ap

6. The ratio of the length of a vertical rod and the length of its shadow is 1: √ 3 . Find the angle
of elevation of the Sun at that moment. (2020) Ev
√
7. The ratio of the height of a tower and the length of its shadow on the ground is 3 :1. What
is the angle of elevation of the sun? (Delhi 2017)
√
8. If a tower 30 m high, casts a shadow 10 3 m long on the ground, then what is the angle of
elevation of the sun? (AI 2017)
9. In the given figure, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the
horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the ladder.

(Use √ 3 =1.73) (Delhi 2016)

10. A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the
ladder is 2.5 m away from the wall, find the length of the ladder. (AI 2016) Ap
√
11. An observer, 1.7 m tall, is 20 3 m away from a tower. The angle of elevation from the eye
of observer to the top of tower is 30°. Find the height of the tower. (Foreign 2016) Ap
12. The tops of two towers of height x and y, standing on level ground, subtend angles of 30°
and 60° respectively at the centre of the line joining their feet, then find x:y.
(Delhi 2015)

13. In the given figure, a tower AB is 20 m high and BC, its shadow on the ground, is 20 √3 m
long. Find the Sun's altitude. (AI 2015)

√
14. A pole casts a shadow of length 2 3 m on the ground, when the sun's elevation is 60°. Find
the height of the pole. (Foreign 2015)
SA I (2 marks)
15. The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is
supporting the disc as shown in the figure. If AC = 1.5 m long and CD = 3 m, then find
(i) tanθ (ii) secθ +cosecθ (2020) Ap

SA II (3 marks)
16. Two boats are sailing in the sea 80 m apart from each other towards a cliff AB. The angles of
depression of the boats from the top of the cliff are 30° and 45° respectively, as shown in
figure. Find the height of the cliff.
 80 m
(Term II, 2021-22)
17. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle
of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m
high, then find the height of the building. (Term II, 2021-22)
18. In figure, AB is tower of height 50 m. A man standing on its top, observes two cars on the
opposite sides of the tower with angles of depression 30° and 45° respectively. Find the
distance between the two cars.

(Term II, 2021-22)

19. An aeroplane when flying at a height of 3125 m from the ground passes vertically below
another plane at an instant when the angles of elevation of the two planes from the same
point on the ground are 30° and 60° respectively. Find the distance between the two planes
at that instant. (Term II, 2021-22)
20. The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's
altitude is 30° than when it is 60°. Find the height of the tower. (Term II, 2021-22 C)
21. The tops of two poles of heights 20 m and 28 m are connected with a wire. The wire is
inclined to the horizontal at an angle of 30°. Find the length of the wire and the distance
between the two poles. (Term II, 2021-22)
22. Two men on either side of a cliff 75 m high observe the angles of elevation of the top of the
cliff to be 30° and 60°. Find the distance between the two men. (Term II, 2021-22)
 Two men on either side of a 75 m high building and in line with base of building observe the
angles of elevation of the top of the building as 30° and 60°. Find the distance between the
√
two men. (Use 3 =1.73) (Foreign 2016)
23. From a point on a bridge across a river, the angles of depression of the banks on opposite
sides of the river are 30° and 45°. If the bridge is at a height of 8 m from the banks, then find
the width of the river. (Term II, 2021-22)

24. A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The
angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the
boat in m/h. (Delhi 2017)
25. From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and
the angle of depression of its foot is 45°. Find the height of the tower.
(NCERT Exemplar, Delhi 2017)
26. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of
elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find
the distance of the hill from the ship and the height of the hill. (AI 2016)
27. The angles of depression of the top and bottom of a 50 m high building from the top of a
tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance
√
between the tower and the building. (Use 3 =1.73). (Delhi 2016)
28. A 7 m long flagstaff is fixed on the top of a tower standing on the horizontal plane. From a
point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60°
and 45° respectively. Find the height of the tower correct to one place of decimal.
√
(Use 3 =1.73). (Foreign 2016)
29. An aeroplane, when flying at a height of 4000 m from the ground passes vertically above
another aeroplane at an instant when the angles of elevation of the two planes from the
same point on the ground are 60° and 45° respectively. Find the vertical distance between
√
the aeroplanes at that instant. (Take 3 =1.73) (Foreign 2016)
30. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle
of elevation of the top of the tower from the foot of the building is 45°. If the tower is 30 m
high, find the height of the building. (Delhi 2015) Ap
31. The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of
15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant

height of 1500 √ 3 m, find the speed of the plane in km/hr. (AI 2015)
32. From the top of a tower of height 50 m, the angles of depression of the top and bottom of a
pole are 30° and 45° respectively. Find
(i) how far the pole is from the bottom of a tower
√
(ii) the height of the pole. (Use 3 =1.732) (Foreign 2015)
33. Two ships are there in the sea on either side of a light house in such a way that the ships and
the light house are in the same straight line. The angles of depression of two ships as
observed from the top of light house are 60° and 45°. If the height of the light house is 200
√
m, find the distance between the two ships. [Use 3 =1.73] (Delhi 2014) Ap
34. The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30
seconds the angle of elevation becomes 30°. If the aeroplane is flying at a constant height of
√
3000 3 m, find the speed of the aeroplane. (Al 2014)
35. From the top of a 60 m high building, the angles of depression of the top and the bottom of

a tower are 45° and 60° respectively. Find the height of the tower. [Take √ 3 =1.73].
(Al 2014) Ap
36. Two ships are approaching a light-house from opposite directions. The angles of depression
of the two ships from the top of the light-house are 30° and 45°. If the distance between the
√
two ships is 100 m, find the height of the light-house. [Use 3 =1.732] (Foreign 2014)
LA (4/5/6 marks)
37. A straight highway leads to the foot of a tower, A man standing on the top of the 75 m high
observes two cars at angles of depression of 30° and 60° which are approaching the foot of
the tower. If one car is exactly behind the other on the same side of the tower, find the
√
distance between the two cars. (Use 3 =1.73). (2023)
38. From the top of a 7 m high building the angle of elevation of the top of a cable tower is 60°
and the angle of depression of its foot is 30°. Determine the height of the tower.(2023)
39. A ladder set against a wall at an angle 45° to the ground. If the foot of the ladder is pulled
away from the wall through a distance of 4 m, its top slides a distance of 3 m down the wall
making an angle 30° with the ground. Find the final height of the top of the ladder from the
ground and length of the ladder. (2023)
40. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is
60°. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is

45°. Find the height of the tower PQ and the distance PX. (Use √ 3 = 1.73)
(Term II, 2021-22, AI 2016)
41. The straight highway leads to the foot of a tower. A man standing at the top of the tower
observes a car at an angle of depression of 30°, which is approaching the foot of the tower
with a uniform speed. Ten seconds later the angle of depression of the car is found to be
60°. Find the time taken by the car to reach the foot of the tower from this point.
(Term II, 2021-22)
42. Case Study: Kite festival
Kite festival is celebrated in many countries at different times of the year. In India, every
year 14th January is celebrated as International Kite Day. On this day many people visit India
and participate in the festival by flying various kinds of kites.
The picture given below, shows three kites flying together.
 In Fig. the angles of elevation of two kites (Points A and B) from the hands of a man (Point C)
are found to be 30° and 60° respectively. Taking AD = 50 m and B = 60 m, find
(i) the lengths of strings used (take them straight for kites A and B as shown in figure.
(ii) the distance 'd' between these two kites. (Term II, 2021-22)
43. A man on the top of a vertical tower observes a car moving at a uniform speed coming
directly toward it. If it takes 18 minutes for the angle of depression to change from 30° to
60°, how soon after this will the car reach the tower? (2021C)
44. A girl on a ship standing on a wooden platform, which is 50 m above water level, observes
the angle of elevation of the top of a hill as 30° and the angle of depression of the base of
the hill as 60°. Calculate the distance of the hill from the platform and the height of the hill.
(2021 C)
45. From a point on the ground, the angles of elevation of the bottom and the top of a
transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find
√
the height of the tower. (Use 3 = 1.73) (2020) Ap
46. A statue 1.6 m tall, stands on the top of a pedestal. From a point on the ground the angle of
elevation of the top of the statue is 60° and from the same point the angle of elevation of
√
the top of the pedestal is 45°. Find the height of the pedestal. (Use = 3 = 1.73) (NCERT,
2020) (Ap)
47. The angles of depression of the top and bottom of a 8 m tall building from the top of a tower
are 30° and 45° respectively. Find the height of the tower and the distance between the
tower and the building. (2019C)
48. As observed from the top of a lighthouse, 75 m high from the sea level, the angles of
depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same
side of the lighthouse, find the distance between the two ships. (2019C)
49. A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the
angle of elevation of the top of the light house from 60° to 30°. Find the speed of the boat in
√
metres per minute. [Use 3 =1.732] (Delhi 2019) Cr
50. Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an
elevation of 30°. Deepak standing on the roof of a 50 m high building, finds the angle of
elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find
the distance of the bird from Deepak. (2019)
51. Two poles of equal heights are standing opposite each other on either side of the road,
which is 80 m wide. From a point between them on the road, the angles of elevation of the
top of the poles are 60° and 30° respectively. Find the height of the poles and the distances
of the point from the poles. (NCERT, Delhi 2019) Ap
OR
 Two poles of equal heights are standing opposite to each other on either side of the road
which is 80 m wide. From a point P between them on the road, the angle of elevation of the
top of a pole is 60° and the angle of depression from the top of another pole at point P is
30°. Find the heights of the poles and the distances of the point P from the poles.
(Foreign 2015)
52. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an
elevation of 30°. A girl standing on the roof of a 20 m high building, finds the elevation of the
same bird to be 45°. The boy and the girl are on the opposite sides of the bird. Find the
distance of the bird from the girl. (Given √ 2 =1.414) (Al 2019) Ap
53. The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of
30 seconds, the angle of elevation changes to 30°. If the plane is flying at a constant height
√
of 3600 3 metres, find the speed of the aeroplane. (Al 2019) Ev
54. As observed from the top of a 100 m high light house from the sea-level, the angles of
depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same
√
side of the light house, find the distance between the two ships. [Use 3 = 1.732]. (2018)
55. The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake
is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the
cloud from the surface of water. (Delhi 2017)
56. Two points A and B are on the same side of a tower and in the same straight line with its
base. The angles of depression of these points from the top of the tower are 60° and 45°
respectively. If the height of the tower is 15 m, then find the distance between these points.
(Delhi 2017)Ev
57. An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles
of depression from the aeroplane of two points on both banks of a river in opposite

directions are 45° and 60° respectively. Find the width of the river. [Use √ 3 =1.732]
(AI 2017)
58. A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of
elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at
a constant height from the ground. After 2 seconds, the angle of elevation of the bird from
√
the same point is 30°. Find the speed of flying of the bird. (Take 3 =1.732). (Delhi 2016).
59. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m
from the base of the tower and in the same straight line with it are 60° and 30° respectively.
Find the height of the tower. (Delhi 2016)
60. As observed from the top of light house, 100 m high above sea level, the angles of
depression of a ship, sailing directly towards it, changes from 30° to 60°. Find the distance
√
travelled by the ship during the period of observation. (Use 3 =1.73). (AI 2016)
61. From a point on the ground, the angle of elevation of the top of a tower is observed to be
60°. From a point 40 m vertically above the first point of observation, the angle of elevation
of the top of the tower is 30°. Find the height of the tower and its horizontal distance from
the point of observation. (Al 2016) Ap
62. A vertical tower stands on a horizontal plane and surmounted by a flagstaff of height 5 m.
From a point on the ground the angles of elevation of the top and bottom of the flagstaff are
60° and 30° respectively. Find the height of the tower and the distance of the point from the

tower. (Take √ 3 =1.732) (Foreign 2016) Ap

 OR
From a point P on the ground the angle of elevation of the top of a tower is 30° and that of
the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m,
find the height of the tower. (Delhi 2015)
63. At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is
30°. The angle of depression of the reflection of the cloud in the lake, at A is 60°. Find the
distance of the cloud from A. (Al 2015) Ap
64. The angles of elevation and depression of the top and the bottom of a tower from the top of
a building, 60m high, are 30° and 60° respectively. Find the difference between the heights
of the building and the tower and the distance between them. (Delhi 2014)
65. The angle of elevation of the top of a tower at a distance of 120 m from a point A on the
ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower,
√
at A is 60°, then find the height of the flagstaff. [Use 3 =1.73]. (AI 2014).
66. The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle
of depression of the foot of the chimney from the top of the tower is 30°. If the height of the
tower is 40 m, find the height of the chimney. According to pollution control norms, the
minimum height of a smoke emitting chimney should be 100 m. State if the height of the
above mentioned chimney meets the pollution norms. What value is discussed in this
question? (Foreign 2014)
 Sample Questions

SA II (3 marks)
1. The Two vertical poles of different heights are standing 20m away from each other on the
level ground. The angle of elevation of the top of the first pole from the foot of the second
pole is 60° and angle of elevation of the top of the second pole from the foot of the first pole

is 30°. Find the difference between the heights of two poles. (Take √ 3 = 1.73)
(Term II, 2021-22)
2. A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. The angle of
elevation of the top of the building from his eye is 60°. Calculate the height of the building.
√
(Take 3 = 1.73) (Term II, 2021-22)
3. If the angles of elevation of the top of the candle from two coins distant 'a' cm and 'b' cm
(a> b) from its base and in the same straight line from it are 30°and 60°, then find the height
of the candle. (2020-21)

LA (4/5/6 marks)
4. Case study: We all have seen the airplanes flying in the sky but might have not thought of
how they actually reach the correct destination. Air Traffic Control (ATC) is a service
provided by ground-based air traffic controllers who direct aircraft on the ground and
through a given section of controlled airspace, and can provide advisory services to aircraft
in non-controlled airspace. Actually, all this air traffic is managed and regulated by using
various concepts based on coordinate geometry and trigonometry.

At a given instance, ATC finds that the angle of elevation of an airplane from a point on the
ground is 60°. After a flight of 30 seconds, it is observed that the angle of elevation changes
√
to 30°. The height of the plane remains constantly as 3000 3 m.
Use the above information to answer the questions that follow:
(i) Draw a neat labelled figure to show the above situation diagrammatically.
(ii) What is the distance travelled by the plane in 30 seconds?
OR
√
Keeping the height constant, during the above flight, it was observed that after 15( 3 -1)
seconds, the angle of elevation changed to 45°. How much is the distance travelled in that
duration?
(iii) What is the speed of the plane in km/hr? (2022-23)
5. Case study: Trigonometry in the form of triangulation forms the basis of navigation, whether
it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth
with the help of satellites.
A guard, stationed at the top of a 240 m tower, observed an unidentified boat coming
towards it. A clinometer or inclinometer is an instrument used for measuring angles or
slopes (tilt). The guard used the clinometer to measure the angle of depression of the boat
coming towards the lighthouse and found it to be 30°.

(Lighthouse of Mumbai Harbour. Picture credits - Times of India Travel)

(i) Make a labelled figure on the basis of the given information and calculate the distance of
the boat from the foot of the observation tower.
(ii) After 10 minutes, the guard observed that the boat was approaching the tower and its
√
distance from tower is reduced by 240( 3 -1)m. He immediately raised the alarm. What
was the new angle of depression of the boat from the top of the observation tower?
(Term II, 2021-22)
6. The two palm trees are of equal heights and are standing opposite each other on either side
of the river, which is 80 m wide. From a point O between them on the river the angles of
elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees
and the distances of the point 0 from the trees. (2020-21)
7. The angles of depression of the top and bottom of a building 50 meters high as observed
from the top of a tower are 30° and 60° respectively. Find the height of the tower, and also
the horizontal distance between the building and the tower. (2020-21)

Self Assessment

Case Based Objective Questions (4 marks)

1. Read the passage given below and answer the following questions.
Fire Incident
There is fire incident in the house. The house door is locked so, the fireman is trying to enter
the house from the window. He place the ladder against the wall such that its top reaches
the window as shown in the figure.
 Based on above information, attempt any 4 out of 5 sub parts.
(i) If window is 6 m above the ground and angle made by the foot of ladder to the ground is
30°, then length of the ladder is
(a) 8 m (b) 10 m (c) 12 m (d) 14 m
(ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to
be 30°, then length of the ladder is
10 15
m m
(a) 5 m (b) √ 3 (c) √ 2 (d) 20 m
(iii) If fireman place the ladder 2.5 m away from the wall and angle of elevation is observed
√
to be 60°, then find the height of the window. (Take 3 =1.73)
(a) 4.325 m (b) 5.5 m (c) 6.3 m (d) 2.5 m
(iv) If the height of the window is 8 m above the ground and angle of elevation is observed
to be 45°, then horizontal distance between the foo of ladder and wall is
(a) 2 m (b) 4m (c) 6 m (d) 8 m
(v) If the fireman gets a 9 m long ladder and window is at 6 m height, then how far should
the ladder be placed?

(a) 5 m √
(b)3 5 m (c) 3m (d) 4m
Multiple Choice Questions (1 mark)
2. The tower and its shadow are equal in length, then find the angle of elevation of the sun.
(a) 30° (b) 60° (c) 90° (d) 45°
√
3. A lamp post 5 3 m high casts a shadow 5 m long the ground. The sun's elevation at this
moment is
(a) 30° (b) 45° (c) 60° (d) 90°
4. From a top of pillar, which is 35 m high above the water, the angle of depression of a boat is
45°. Find the horizontal distance of the boat from the pillar.
35
(a) 35 m (b) 17.5 m (c) 70 m (d) √ 3 m
5. The angle of depression from the top of a tower, 15 m high at a point on the ground, is 30°.
The distance of the point from the top of the tower is

(a) 30 m (b) 15 m √
(c) 30 3 m √
(d)15 3 m
6. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away
from the foot of the tower is 45°. The height of the tower (in metres) is

(a) 15 (b) 30 √
(c) 30 3 (d) 10 3 √
OR
A ladder makes an angle of 60° with the ground, when placed along a wall. If the foot of the
ladder is 8 m away from the wall, then the length of the ladder is

(a) 4 m (b) 8 m √
(c) 8 3 m (d) 16 m
7. From the given figure, the angle of depression of point C from the point P is
 (a) 45° (b) 90° (c) 75° (d) 30°
VSA Type Questions (1 mark)
8. The height of a pillar is 8 m. What is the length of its shadow, when sun's altitude is 30°?
9. Find the length of a ladder which is leaning against a vertical wall by making an angle of 30°
with the ground and whose foot is 6 m away from the wall.
10. A kite is flying at a height of 100 m from the ground. It is attached to a string inclined at an
angle of 45° to the horizontal. Find the length of the string.
√
11. If the length of the shadow of a vertical flag staff is 1/ 3 of its height, then find the sun's
angle of elevation.
OR
The angle of depression of a car standing on the ground from the top of a 75 m tower, is 30°.
Find the distance of the car from the base of the tower (in metres).
12. If the angle of elevation of the sun is 30°, then find the length of the shadow cast by a tower
of 150 feet height.
SA I Type Questions (2 marks)
13. A wall 8 m long casts a shadow 5 m long. At the same time, a tower casts a shadow 50 m
long, then find the height of tower.
OR
A man sitting on the top of a tower of height 30 m observes the angle of depression of a dog
sitting on the ground as 60°. Find the distance between the foot of the tower and the dog.
√
(Use 3 = 1.732)
14. The tops of two towers of height 48 m and 60 m are connected by a string. If the string is
making an angle of 60° with horizontal, then find the length of the string.
15. From a bridge, 35 m high, the angle of depression of a boat is 45°. Find the horizontal
distance of the boat from the bridge.
16. An aeroplane at an altitude of 400 m observes the angles of depression of opposite points
on the two banks of a river to be 45° and 60°. Find width of the river.
SA II Type Questions (3 marks)
17. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of
elevation of the top of a hill as 60° and angle of depression of the base of the hill as 30°. Find
the horizontal distance of the hill from the ship and height of the hill.
18. On the same side of a tower, two objects are located. When observed from the top of the
tower, their angles of depression are 45° and 60°. If the height of the tower is 100 m, find
√
the distance between the objects. [Use 3 =1.73]
OR
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is
60°. At a point R, 40 m vertically above X, the angle of elevation is 45°. Find the height of the
tower PQ.
19. Two ships are anchored on opposite sides of a lighthouse. Their angles of depression as
observed from the top of the lighthouse are 30° and 60°. The line joining the ships passes
through the foot of the lighthouse. If the height of the lighthouse is 100 m, find the distance
√
between the ships. (Use 3 = 1.732)
20. Two pillars of equal heights stand on either side of a road which is 160 m wide. At a point on
the road between the pillars, the angles of elevation of the tops of the pillars are 60° and
30°. Find the height of each pillar and the position of the point on the road.
21. From the top of a hill, the angles of depression of two consecutive kilometre stones D and C
due west are found to be 30° and 60° respectively. Find the height of the hill.
Case Based Questions (4 marks)
22. An electrician has to repair an electric fault on the pole of height of 8 m. He needs to reach a
point 2 m below the top of the pole to undertake the repair work.

Based on given information, answer the following questions.

(i) What should be the length of ladder, so that it makes an angle of 60° with base?
(ii) What will be the measure of BCD when BD and CD are equal?
(iii) If an electrician wants to reach 4 m below the top of the pole using a ladder which is
√
4 3 m away from it, then what angle does it make with the base?
OR
If an electrician want to reach the top of the pole of height 12 m, with making an angle 60°
with base, then find the required length of ladder.
LA Type Questions (4/5/6 marks)
23. A boy is standing on the ground and flying a kite with a string of length 150 m at an angle of
elevation of 30°, another boy is standing on the roof of a 25 m high building and is flying his
kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the
length of the string (in metres corrected to two decimal places) the second boy must have so
that the two kites meet. (Use √ 2 = 1.4142)
24. A man on the top of a vertical tower observes a car moving at a uniform speed coming
directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to
45°, how soon after this, will the car reach the tower? Give your answer to the nearest
seconds.
25. The angle of elevation of the top of a tower from a point A due south of the tower is a and
from B due east of the tower is b. If AB = d, show that the height of the tower is
d
√ cot 2
α+ cot 2 β
OR
Two stations due south of a leanings tower which leans towards the north are at distances a
and b from its foot. If α, β be the elevations of the top of the tower from these stations,
b cot α−a cot β
cot θ=
prove that its inclination θ to the horizontal is given by b−a .