CH-9 Super 30

Super 30
Questions
Some Application of Trigonometry
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Super 30 Questions
Some Application of Trigonometry
1. The length of the shadow of a tower on the plane ground is √3 times the height of
the tower. The angle of elevation of sun is:
(A) 45° (B) 30° (C) 60° (D) 90°
2. The tops of the poles of height 16 m and 10 m are connected by a wire of length l
metres. If the wire makes an angle of 30° with the horizontal, then 𝑙 =
(A) 26 𝑚 (B) 16 𝑚 (C) 12 𝑚 (D) 10 𝑚
3. 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, then the length of the ladder is
(A) 3 𝑚 (B) 4 𝑚 (C) 5 𝑚 (D) 6 𝑚
4. If a tower is 30 m high, casts a shadow 10√3𝑚 long on the ground, then the angle
of elevation of the sun is
(A) 30° (B) 45° (C) 60° (D) 90°
5. A tower is 50 m high. When the sun’s altitude is 45° then what will be the length of
its shadow?
50
6. The length of shadow of a pole 50 m high is 𝑚 find the sun’s altitude.
√3
7. In the figure, find the value of BC.
8. In the figure, find the value of CF.

9. The shadow of a vertical tower on level ground increases by 10 m when the
altitude of the sun changes from 45° to 30°. Find the height of the tower.[𝑈𝑠𝑒 √3 =
1.73]
10. An aeroplane at an altitude of 200 m observes angles of depression of opposite
points on the two banks of the river to be 45° and 60°, find the width of the river.
[𝑈𝑠𝑒 √3 = 1.732]
11. The angle of elevation of a tower at a point is 45°. After going 40 m towards the
foot of the tower, the angle of elevation of the tower becomes 60°. Find the height of
the tower. [𝑈𝑠𝑒 √3 = 1.732]
12. The upper part of a tree broken over by the wind makes an angle of 30° with the
ground and the distance of the foot of the tree from the point where the top touches
the ground is 25 m. What was the total height of the tree?
13. A vertical flagstaff stands on a horizontal plane. From a point 100 m from its foot,
the angle of elevation of its top is found to be 45°. Find the height of the flagstaff.
14. The length of a string between kite and a point on the ground is 90 m. If the string
3
makes an angle 𝛼 with the level ground and sin 𝛼 = . Find the height of the kite.
5
There is no slack in the string.
15. An aeroplane, when 3000 m high, passes vertically above another plane at an
instant when the angle of elevation of two aeroplanes from the same point on the
ground are 60° and 45° respectively. Find the vertical distance between the two
planes. [𝑈𝑠𝑒 √3 = 1.732]
16. From the top of a 7 m high building, the angle of elevation of the top of the tower
is 60° and the angle of depression of the foot of the tower is 45°. Find the height of
the tower.
17. A man standing on the deck of a ship, 10 m above the water level observes the
angle of elevation of the top of a hill as 60° and angle of depression of the bottom of
the hill as 30°. Find the distance of the hill from the ship and height of the hill.
18. From a window 60 m high above the ground of a house in a street, the angle of
elevation and depression of the top and the foot of another house on the opposite
side of the street are 60° and 45° respectively. Show that the height of opposite
house is 60(1 + √3) metres.

19. 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 m, find the speed in km/hour of the plane.
20. A bird is sitting on the top of a tree, which is 80 m high. The angle of elevation of
the bird, from a point on the ground is 45°. The bird flies away from the point of
observation horizontally and remains at a constant height. After 2 seconds, the angle
of elevation of the bird from the point of observation becomes 30°. Find the speed of
flying of the bird. [𝑈𝑠𝑒 √3 = 1.732]
21. The angles of elevation of the top of a tower from two points on the ground at
distances 9 m and 4 m from the base of the tower are in the same straight line with it
are complementary. Find the height of the tower.
22. An observer from the top of a light house, 100 m high above sea level, observes
the angle of depression of a ship, sailing directly towards him, changes from 30° to
60°. Determine the distance travelled by the ship during the period of observation.
23. A 1.2m tall girl spots a balloon on the eve of Independence Day, moving with the
wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation
of the balloon from the girl at an instant is 60°. After some time, the angle of
elevation reduces to 30°. Find the distance travelled by the balloon.
24. Two pillars of equal heights stand on either side of a roadway 150 m wide. From
a point on the roadway between the pillars, the angles of elevation of the top of the
pillars are 60° and 30°. Find the height of pillars and the position of the point.
25. A moving boat is observed from the top of a 150 m high cliff moving away form
the cliff. The angle of depression of the boat changes form 60° to 45° in 2 minutes.
Find the speed of the boat in m/h.
26. 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, find
(i) tan 𝜃 (ii) sec 𝜃 + cosec 𝜃.

27. The angle of elevation of a cloud from a point h metres above the surface of a
lake is θ and the angle of depression of its reflection in the lake is 𝜙. Prove that the
𝑡𝑎𝑛𝜙+tan 𝜃
height of the cloud above the lake is ℎ ( ).
tan 𝜙−tan 𝜃
28. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag
staff of height ℎ. At a point on the plane, the angles of elevation of the bottom and
the top of the flag staff are α and β, respectively. Prove that the height of the tower
ℎ tan 𝛼
is ( ).
tan 𝛽−tan 𝛼
29. A window of a house is h metres above the ground. From the window, the angles
of elevation and depression of the top and the bottom of another house situated on
the opposite side of the lane are found to be α and β, respectively. Prove that the
height of the other house is h ( 1 + tan α cot β ) metres.
30. The lower window of a house is at a height of 2 m above the ground and its upper
window is 4 m vertically above the lower window. At certain instant the angles of
elevation of a balloon from these windows are observed to be 60o and 30o,
respectively. Find the height of the balloon above the ground.
ANSWER’S
Q1. B Q15. 1268 m
Q2. C Q16. 7(√3) + 1 m
Q3. C Q17. 10√3𝑚, 40 𝑚
Q4. C Q19. 864 km/hr
Q5. 50 m Q20. 29.28 m
Q6. 60° Q21. 6 𝑚
Q7. 130 𝑚 Q22. 115.46 m
Q8. 25 m Q23. 58√3
Q9. 13.65 𝑚 Q24. ℎ𝑒𝑖𝑔ℎ𝑡 = 64.95 𝑚,
Q10. 315.46 m Q25. 1902 𝑚/ℎ (Approx)
Q11. 94.64 m 1
Q26. (i) tan 𝜃 =
Q12. 25√3 m √3
2
Q13. 100 m (ii) sec 𝜃 + 𝑐𝑜𝑠𝑒𝑐 𝜃 = +2
√3
Q14. 54 𝑚 Q30. 8 m

If there is any doubt regarding to these Questions you can resolve by seeing this
video. Here is the link of the Video
https://youtu.be/EnbqkQvqoOM?si=Nmja6kVJetrwiu8u
Chapter-9 One shot Lecture:- https://youtu.be/ubJvgGn5jZ4?si=IXI9__iHZlx_2rGz

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Super 30

Some Application of Trigonometry

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7. In the figure, find the value of BC.

8. In the figure, find the value of CF.

GYAANI KEEDA bhattdeepak454 https://t.me/gyannikeedamaths

GYAANI KEEDA bhattdeepak454 https://t.me/gyannikeedamaths

GYAANI KEEDA bhattdeepak454 https://t.me/gyannikeedamaths

GYAANI KEEDA bhattdeepak454 https://t.me/gyannikeedamaths

GYAANI KEEDA bhattdeepak454 https://t.me/gyannikeedamaths

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