RATIONAL TUTORIALS

Std 10 : Maths(S)
PP - APPLICATION OF TRIGONOMETRY
Section A
//X
• Write the answer of the following questions. [Each carries 1 Mark] [23]
1. ) A 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. 12
seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to
reach the tower.
2. 14) A 1.3 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 9.13 m from
the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After
some time the angle of elevation reduces to 30°. Find the distance travelled by the balloon during this
interval.
3. ) From a hill, 200 m high, the angles of depression of two cars situated on the same side are 30° and
60°. Find the distance between the two cars.
4. 12) From a top of the house, 10 m high, the angle of elevation of the tower is 60° and the angle of
depression of the tower is 45°. Find the height of the tower.
5. ) A tree stands vertical on the bank of the river. From the other side of the bank of the river, the angle of
elevation of the top of the tree is 60°. On walking 40 m behind this point, the angle of elevation finds to
be 30°. Find the height of the tree and the width of the river. Take( 3 = 1.73 )
6. 10) Two poles of equal heights are standing opposite each other on either side of the road which is 100 m
wide. From a point between them on the road, the angle of the elevation of the top of the poles are
60° and 30° respectively. Find the height of the poles and the distance of the point from the nearest pole.
7. The angle of elevation of the top of the tower from the foot of a house is 60° and the angle of elevation
of the top of the house from the foot of the tower is 30°. If the height of the tower is 60 m then find the
height of the house.
8. A statue of Sardar Patel, 1.46 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.
9. A statue, 36.50 m tall stands on the top of a pedestal. From a point on the ground the angles of elevation
of the top and bottom of the statue are respectively 60° and 45°. Find the height of the statue.
( Take 3 = 1.73 )
10. A 1.5 m tall boy is standing at some distance from a 28.5 m tall building. The angle of elevation from
his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the
distance he walked towards the building (Take 3 = 1.73 )
11. A kite is flying from the ground level attached a string of length 100 m. A string inclined at 30° to the
horizontal. Find the height of the kite assuming that there is no slack in the string.
12. There is a temple on the bank of the river. From the point opposite to the bank of the river, the angle
of elevation of the top of the temple is 30°. If the width of the river is 34.64 m, find the height of the
temple.
13. A contractor plans to install two slides for the children to play in a park. For the children below the age
of 5 years, he prefers to have a slide whose top is at a height of 2m and inclined at an angle of 30°
to the ground. Where as for elder children, he wants to have a steep slide at a height of 3.9 m and
MATHEMATICS BY K T JOSHI
inclined at an angle of 60° to the ground what should be the length of the slide in each case ?
 A contractor plans to install two slides for the children to play in a park. For the children below the age
of 5 years, he prefers to have a slide whose top is at a height of 2m and inclined at an angle of 30°
to the ground. Where as for elder children, he wants to have a steep slide at a height of 3.9 m and
inclined at an angle of 60° to the ground what should be the length of the slide in each case ?
14. An eucalyptus tree breaks due to the storm and the broken part bends so that the top of the tree touches
the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point
where top touches the ground is 12.11 m. Find the height of the tree.
15. The ladder is placed along a wall such that its upper end is touching top of the 3m high wall. If its bottom
makes an angle of measure 30° with the ground then find the height of the ladder.

16. There are two points A and B on the ground at East and West direction of the tower. From the top of
the tower, the angles of depression of the points A and B are respectively a and b. b > a then the
distance of the point .......... is more from the tower.
17. A ladder is placed along the wall. The foot of the ladder is 1.5 m away from the wall. If the length
of the ladder is 3m, find the angle makes by the ladder with the ground.
18. A ladder is placed along a wall such that its upper end is touching the wall at 4m high. The length
of the ladder is 5m. Then the foot of the ladder is .......... m away from the ground.
P
(A) 3
q
(B) 4
m

4m
5

(C) 5

(D) 6 Q R

19. When the angle of elevation of the sun decreases from 30° to 45°, the length of the shadow of the
building decreases x m. If the height of the building is 100 m, find the value of x.
20. From the bottom of the house A, the angle of elevation of the top of the house B is 45° and from
the bottom of the house B, the angle of elevation of the top of the house A is 65°. Then
(A) The height of B is more than the height of A.
(B) The heights of A and B are equal.
(C) The height of A is more than the height of B.
(D) None of these.
21. There are two poles of the height 18 m and 12 m. A steel wire tied to top of the poles. If the wire
makes an angle of 30° with the horizontal line, find the length of the wire.
22. A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot
of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the
tower.
23. The height of the tower AB in the given figure is .........
A
Tower

40 m
30°
B C

Section B
//X
• Write the answer of the following questions. [Each carries 2 Marks] [30]

24. A ladder is placed along a wall 3 m high such that its upper end is touching the top of the wall. The
foot of the ladder makes an angle 30° with the ground then find the length of the ladder.
25. From the top of the house, the angle of depression of the man standing 10 m away from the house is
found to be 45°. Find the height of the house.
MATHEMATICS BY K T JOSHI
 From the top of the house, the angle of depression of the man standing 10 m away from the house is
found to be 45°. Find the height of the house.
26. The height of the tower is 30 m when the angle of elevation of the sun is 45°, find the length of its
shadow.
27. From a particular point on the bank of the river, the angle of elevation of the top of the temple
situated on the opposite bank of the river is found to be 30°. If the height of the temple is 20 m, find
the width of the river.
28. A vertical pole stands on a horizontal plane. A wire with 7 m length tied the top of the pole with a
point on the ground. If the wire makes an angle of measure 30°, find the height of the pole.
29. The height of the tower is 6 m and its shadow is 2 3 m long. Find the angle of elevation of the sun.

30. The ratio of the height of the tower and the length of its shadow is 1 : 3 . Find the angle of elevation
of the sun.
31. How many metre one can walk on a slope making an angle 30° with the ground so that he attains the
height ‘a’ metre ?
32. A ladder is placed along the wall. The foot of the ladder is 1.5 m away from the wall. If the length of
the ladder is 3m, find the angle makes by the ladder with the ground.
33. There are two poles of the height 18 m and 12 m. A steel wire tied to top of the poles. If the wire makes
an angle of 30° with the horizontal line, find the length of the wire.
34. From the top of the tower, 30 m high, the angle of depression of a ship is 60°. Find the distance of the
ship from the tower.
35. From the top of the building h m high, the angle of depression of an object on the ground is q. Find
the distance of this object from the building.
36. The height of the hill is 30 m from the top of the hill, the angle of elevation of the top of the tower
is equal to the angle of depression of the bottom of the tower. Find the height of the tower.
37. When the angle of elevation of the sun decreases from 30° to 45°, the length of the shadow of the
building decreases x m. If the height of the building is 100 m, find the value of x.
38. In a right angle triangle the length of one side is half the length of the hypotenuse. Find the angle
between the side and the hypotenuse.

Section C
//X
• Write the answer of the following questions. [Each carries 3 Marks] [12]

39. An eucalyptus tree with 15 m high breaks due to the storm at 5m high from the ground and its broken
part bends so that the top of tree touching the ground. Find the angle makes by the parts with top
of the tree with the ground.
40. .1) A house is surmounted by a vertical flagstaff. At a point on the plane 15 m away from the tower,
an observer notice that the angles of elevation of the top of the house and flagstaff are respectively
45° and 60°. Find the height of the flagstaff.
41. .2) The height of the hill is 340 m. As observed from the top of the hill, the angle of depression of two
houses situated at East and west side of the hill is found to be 30° and 60° respectively. Find the
distance between the two houses.
42. The angles of elevation of the top of a tower from two points at a distance of 3 m and 12 m from the
base of the tower and in the same straight line with it are complementary. Prove that the height of the
tower is 6 m.

MATHEMATICS BY K T JOSHI
 Section D
//X
• Write the answer of the following questions. [Each carries 4 Marks] [24]

43. 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 45°. Determine the height of the tower.
44. .1) When the angle of elevation of the sun is 30°, the length of the shadow of the tower is 27 m. Find
the length of the shadow of the tower, if the angle of elevation of the sun is 60°.
45. .2) From the top of the hill, 200 m high, the angles of depression of two vehicles, same side of the hill,
are found to be 60° and 30°. Find the distance between these two vehicles.
46. An observer spots a balloon moving with the wind in a horizontal line at a height of 105 m from the
ground. The angle of elevation of the balloon after sometime reduces from 60° to 30°. Find the distance
travelled by the balloon during the interval.
47. From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag
is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°.
Find the length of the flagstaff and the distance of the building from the point P. (You may take 3=
1.732)
48. 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 60° respectively. If the bridge is at a height of 3 m from the banks, find the width
of the river.

MATHEMATICS BY K T JOSHI
 RATIONAL TUTORIALS
Std 10 : Maths(S)
PP - APPLICATION OF TRIGONOMETRY
Section A
//X
• Write the answer of the following questions. [Each carries 1 Mark] [23]
1.

2.

3.

4.

5.

6.

7.

8.

9.

Welcome To Future - Quantum Paper

11.

12.

13.

14.

15.

16.

17.

18.

//X
 Ans : (A)
19.

Welcome To Future - Quantum Paper

//X
 Ans : (C)
21.

22.

23.

Section B
//X
• Write the answer of the following questions. [Each carries 2 Marks] [30]

24.

25.

26.

27.

28.

29.

Welcome To Future - Quantum Paper

31.

32.

Welcome To Future - Quantum Paper

34.

Welcome To Future - Quantum Paper

36.

37.

Welcome To Future - Quantum Paper

Section C
//X
• Write the answer of the following questions. [Each carries 3 Marks] [12]

39.

40.

41.

Welcome To Future - Quantum Paper

Section D
//X
• Write the answer of the following questions. [Each carries 4 Marks] [24]

43.

44.

45.

46.

47.

48.

Welcome To Future - Quantum Paper