CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set 02

Multiple Choice Questions

Question. A pole 6 m high casts a shadow \( 2\sqrt{3} \) m long on the ground, then the Sun’s elevation is 
(a) 60°
(b) 45°
(c) 30°
(d) 90°
Answer: (a) 60°

Question. The length of a string between a kite and a point on the ground is 85 m, if the string makes an angle \( \theta \) with the ground level such that \( \tan \theta = \frac{15}{8} \), then at what height is the kite from the ground? 
(a) 75 m
(b) 79.41 m
(c) 80 m
(d) 72.5 m
Answer: (a) 75 m

Question. A ladder 18 m long makes an angle of 60° with a wall. The height of the point where the ladder reaches the wall is
(a) \( 9\sqrt{3} \) m
(b) \( 18\sqrt{3} \) m
(c) 18 m
(d) 9 m
Answer: (a) \( 9\sqrt{3} \) m

Question. The angle of depression of a car parked on the road from the top of 150 m high tower is 30°. The distance of the car from the tower (in metres) is
(a) \( 50\sqrt{3} \)
(b) \( 150\sqrt{3} \)
(c) \( 150\sqrt{2} \)
(d) 75
Answer: (b) \( 150\sqrt{3} \)

Question. If the angle of elevation of top of a tower from a point on the ground which is \( 20\sqrt{3} \) m away from the foot of the tower is 30°, then the height of the tower is
(a) 60 m
(b) 30 m
(c) 25 m
(d) 20 m
Answer: (d) 20 m

Question. If the angles of elevation of the top of a tower from the two points at a distance of 2 m and 8 m from the base of the tower and in the same straight line with it are 60° and 30°, then the height of the tower is
(a) 3 m
(b) 4 m
(c) 5 m
(d) 6 m
Answer: (b) 4 m

Question. If a 30 m ladder is placed against a 15 m wall such that it just reaches the top of the wall, then the elevation of the wall is equal to
(a) 45°
(b) 30°
(c) 60°
(d) 50°
Answer: (b) 30°

Question. A 1.6 m tall girl stands at distance of 3.2 m from a lamp post and casts shadow of 4.8 m on the ground, then the height of the lamp post is
(a) 8 m
(b) 4 m
(c) 6 m
(d) \( \frac{8}{3} \) m
Answer: (d) \( \frac{8}{3} \) m

Question. An observer 1.6 m tall is \( 20\sqrt{3} \) m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is
(a) 21.6 m
(b) 23.2 m
(c) 24.72 m
(d) None of the options
Answer: (a) 21.6 m

Question. From the top of a 42 m high light house, the angles of depression of two ships that are in a straight line are 60° and 45° respectively. What is the distance between the two ships? (Use \( \sqrt{3} = 1.73 \))
(a) 12.4 m
(b) 17.8 m
(c) 24.2 m
(d) 32.39 m
Answer: (b) 17.8 m

Question. A pole of 6 m high casts a shadow 2 3 m long, then sun’s elevation is
(a) 60°
(b) 45°
(c) 30°
(d) 90°
Answer : A

Question. At some time of the day, the length of the shadow of a tower is equal to height. Then the sun’s altitude at that time is
(a) 30°
(b) 60°
(c) 90°
(d) 45°
Answer : D

Question. The angle of depression of a car standing on the ground, from the top of a 75 m high tower is 30°. The distance of the car from the base of the tower (in m) is:
(a) 25 3
(b) 50 3
(c) 75 3
(d) 150
Answer : C

Question. In the given figure, the angles of depressions from the observing positions O1 and O2 respectively of the object A respectively are

(a) 30°, 45°
(b) 45°, 60°
(c) 60°, 75°
(d) 60°, 30°
Answer : A

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): If the angle of elevation of Sun, above a perpendicular line (tower) decreases, then the shadow of tower increases.
Reason (R): It is due to decrease in slope of the line of sight.
Answer : A

Question. Assertion (A): When we move towards the object, angle of elevation decreases.
Reason (R): As we move towards the object, it subtends large angle at our eye than before.
Answer : D

Answer the following:

Question. A kite is attached to a string. Assuming that there is no slack in the string, find the height of the kite above the level of the ground, if the length of the string is 54 m and it makes an angle of 30° with the ground.
Answer : 27 m

Question. In the given 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.

Answer : 10√3 m

Question. 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?
Answer : 30°

Question. In the given figure, the angle of elevation of the top of a tower AC from a point B on the ground is 60°. If the height of the tower is 20 m, find the distance of the point from the foot of the tower.

Answer : (20/√3)m

Question. A tower stands vertically on the ground. From a point on the ground, which is 15m 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
Answer : In right ΔABC, tan 60° = h/15

⇒ √3 = h/15
∴ h = 15√3 m

Please click on below link to download CBSE Class 10 Application of Trigonometry Worksheet Set B