CBSE Class 10 Mathematics Application of Trigonometry MCQs Set B

Question. 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
(a) 4/√3
(b) 4√3
(c) 2√2
(d) 4

Answer: D

Question. From a point on the ground, which is 15 m away from the foot of a vertical tower, the angle of elevation of the top of the tower, is found to be 60°. The height of the tower (in metres) is
(a) 5√3
(b) 15√3
(c) 15
(d) 7.5

Answer: B

Question. A lamp post 5√3 m high casts a shadow 5 m long on the ground. The Sun’s elevation at this moment is
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: C

Question. 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
(a) 30°
(b) 60°
(c) 45°
(d) 75°

Answer: B

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

Answer: D

Question. The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the Sun’s elevation is 30° than when it was 45°. The height of the tower (in metres) is
(a) (√3 +1) x
(b) (√3 –1) x
(c) 2√3 x
(d) 3√2 x

Answer: A

Question. If two towers of height h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h₁ : h₂ is
(a) 3 : 1
(b) √3 : 1
(c) 1 : √3
(d) 1 : 3

Answer: A

Question. The angle of elevation of a cloud from a point h metres above a lake is θ. The angle of depression of its reflection in the lake is 45°. The height of the cloud (in metres) is
(a) h (1 - tanθ / 1 + tanθ)
(b) h (1 - cotθ / 1 + cotθ)
(c) h (1 + tanθ / 1 - tanθ)
(d) h (1 + cotθ / 1 - cotθ)

Answer: C

Question. The length of 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°

Answer: B

Question. 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

Answer: B

Question. The angle of elevation of the top of a pillar from a point on the ground is 15°. On walking 100 m towards the pillar, the angle of elevation becomes 30°. Find the height of the pillar.
(a) 25 m
(b) 50 m
(c) 50√2 m
(d) 25√2m

Answer: B

Question. The tops of two poles of height 18 m and 10 m are connected by a wire of length l. If the wire makes an angle of 30° with the horizontal, then l is equal to
(a) 26 m
(b) 16 m
(c) 12 m
(d) 10 m

Answer: B

Question. A person walking 20 m towards a chimney in a horizontal line through its base observes that its angle of elevation changes from 30° to 45°. The height of chimney is
(a) (20/√3 +1)m
(b) (20/√3 −1)m
(c) 20( 3 −1)m
(d) None of the options

Answer: B

Question. If the angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β, then the height of the cloud is
(a) h(tanβ + tanα)/tanβ - tanα
(b) h(tanβ - tanα)/(tanβ + tanα)
(c) h/tanβ - tanα
(d) tanβ + tanα/tanβ - tanα

Answer: A

Question. The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100 m from its base is 45°. If the angle of elevation of the top of the complete pillar at the same point is to be 60°, then the height of the incomplete pillar is to be increased by
(a) 100 (√3 +1) m
(b) 100 m
(c) 100√3 m
(d) 100(√3 –1) m

Answer: D

Question. A wall 8 m long casts a shadow 5 m long. At the same time, a tower casts a shadow 50 m long, then the height of tower is
(a) 20 m
(b) 80 m
(c) 40 m
(d) 200 m

Answer: B

Question. From the foot of a pole, the angle of elevation of the top of a tower is 60° and from the top of the pole, the angle of elevation is 30°. If the height of the pole is 25 m, then the height of the tower is
(a) 35 m
(b) 42.5 m
(c) 37.5 m
(d) 27.5 m

Answer: C

Question. The length of a string between a kite and a point on the ground is 85 m. If the string makes an angle q with level ground such that tanθ = 15/8, then how high is the kite?
(a) 75 m
(b) 78.05 m
(c) 226 m
(d) None of the options

Answer: A

Question. Two men standing on opposite sides of a flagstaff measure the angles of elevation of the top of the flagstaff is 30° and 60°. If the height of the flagstaff is 20 m, then approximate distance between the men is (Use √3 = 1.732)
(a) 46.19 m
(b) 40 m
(c) 50 m
(d) 30 m

Answer: A

Question. There are two temples one on each bank of a river just opposite to each other. One temple is 40 m high. As observed from the top of this temple, the angle of depression of the top and foot of the other temple are 30° and 60° respectively. The width of river is
(a) (40√3) m
(b) (40/3) m
(c) (120/√3) m
(d) (80/√3) m

Answer: A

Question. Suppose a straight vertical tree is broken at some point due to storm and the broken part is inclined at a certain distant from the foot of the tree. If the top of broken part of a tree touches the ground at a point whose distance from foot of the tree is equal to height of remaining part, then its angle of inclination is
(a) 30°
(b) 60°
(c) 45°
(d) None of the options

Answer: C

Question. The ratio of the height of a tree and its shadow is 1: 1√3. The angle of the Sun’s elevation is
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: C

Question. A steel pole is 30 m high. To keep the pole upright, one end of a steel wire is tied to the top of the pole while the other end has been fixed on the ground. If the steel wire makes an angle of 45° with the horizontal through the base point of the pole, then find the length of the steel wire.
(a) 30√2 m
(b) 30√3 m
(c) 15 m
(d) 15√2 m

Answer: A

Question. A portion of a 45 m long tree is broken by tornando and the top struck up the ground making an angle of 30° with the ground level. The height of the point where the tree is broken, is equal to
(a) 30 m
(b) 15 m
(c) 10 m
(d) 20 m

Answer: B

Question. A man standing on the deck of a ship, which is 10 m above the water level observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. The distance of the hill from the ship is
(a) 40 m
(b) 10√3 m
(c) 10 m
(d) 20√3m

Answer: B

Question. The length of shadow of a building, when the Sun’s altitude is 60°, is 20 m less than that it was when it was 45°. The height of the building is (Use √3 = 1.732)
(a) 54.48 m
(b) 47.32 m
(c) 64.32 m
(d) 57.48 m

Answer: B

Question. A peacock sitting on the top of a tree observes a serpent on the ground making an angle of depression 30°. If the peacock with a speed of 300 m per minute catches the serpent in 12 seconds, then the height of the tree is
(a) 30 m
(b) 30√3 m
(c) (30/√3)m
(d) 15 m

Answer: A

Question. A bridge across a river makes an angle of 45° with the river bank. If the length of the bridge across the river is 50 m, then what is the width of the river?
(a) 20√2 m
(b) 50√2 m
(c) 25√2 m
(d) 10√2 m

Answer: C

Question. The angle of elevation is always
(a) obtuse angles
(b) acute angles
(c) right angles
(d) reflex angles

Answer: B

Question. If the height of a tree is 6 m, which is broken by wind in such a way that its top touches the ground and makes an angles 30° with the ground. At what height from the bottom of the tree is broken by the wind?
(a) 2 m
(b) 4 m
(c) 8 m
(d) 10 m

Answer: D

Question. A window is 6 m above the ground. A ladder is placed against the wall such that its top reaches the window. If 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

Answer: C

Question. If the height of the window is 8 m above the ground. A ladder is placed against the wall such that its top reaches the window. If angle of elevation is observed to be 45°, then horizontal distance between the foot of ladder and wall is
(a) 2 m
(b) 4 m
(c) 6 m
(d) 8 m

Answer: D

Case Based MCQs

Case I : Read the following passage and answer the questions.

Visit to Temple

There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing on the top of 50 m high temple, observed from the top that angle of depression of the top and foot of other temple are 30° and 60° respectively. (Take √3 = 1.73)

Question. Measure of ∠ADF is equal to
(a) 45°
(b) 60°
(c) 30°
(d) 90°

Answer: C

Question. Measure of ∠ACB is equal to
(a) 45°
(b) 60°
(c) 30°
(d) 90°

Answer: B

Question. Width of the river is
(a) 28.90 m
(b) 26.75 m
(c) 25 m
(d) 27 m

Answer: A

Question. Height of the other temple is
(a) 32.5 m
(b) 35 m
(c) 33.33 m
(d) 40 m

Answer: C

Question. Angle of depression is always
(a) reflex angle
(b) straight
(c) an obtuse angle
(d) an acute angle

Answer: D

Case II : Read the following passage and answer the questions.

Application of Trigonometry for Moving Car

Rohit is standing at the top of the building observes a car at an angle of 30°, which is approaching the foot of the building with a uniform speed. 6 seconds later, angle of depression of car formed to be 60°, whose distance at that instant from the building is 25 m.

Question. Height of the building is
(a) 25√2 m
(b) 50 m
(c) 25√3 m
(d) 25 m

Answer: C

Question. Distance between two positions of the car is
(a) 40 m
(b) 50 m
(c) 60 m
(d) 75 m

Answer: B

Question. Total time taken by the car to reach the foot of the building from starting point is
(a) 4 secs
(b) 3 secs
(c) 6 secs
(d) 9 secs

Answer: D

Question. The distance of the observer from the car when it makes an angle of 60° is
(a) 25 m
(b) 45 m
(c) 50 m
(d) 75 m

Answer: C

Question. The angle of elevation increases
(a) when point of observation moves towards the object
(b) when point of observation moves away from the object
(c) when object moves away from the observer
(d) None of these

Answer: A

Case III : Read the following passage and answer the questions.

Flying Pigeon

A boy 4 m tall spots a pigeon sitting on the top of a pole of height 54 m from the ground. The angle of elevation of the pigeon from the eyes of boy at any instant is 60°. The pigeon flies away horizontally in such a way that it remained at a constant height from the ground. After 8 seconds, the angle of elevation of the pigeon from the same point is 45°. (Take √3 = 1.73)

Question. Find the distance of first position of the pigeon from the eyes of the boy.
(a) 54 m
(b) 100 m
(c) (100/√3)m
(d) 100√3

Answer: C

Question. If the distance between the position of pigeon increases, then the angle of elevation
(a) increases
(b) decreases
(c) remains unchanged
(d) can’t say

Answer: B

Question. Find the distance between the boy and the pole.
(a) 50 m
(b) (50/√3)m
(c) 50√3 m
(d) 60√3 m

Answer: B

Question. How much distance the pigeon covers in 8 seconds?
(a) 12.13 m
(b) 19.60 m
(c) 21.09 m
(d) 26.32 m

Answer: C

Question. Find the speed of the pigeon.
(a) 2.63 m/sec
(b) 3.88 m/sec
(c) 6.7 m/sec
(d) 9.3 m/sec

Answer: A

Assertion & Reasoning Based MCQs

Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given. Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : If the height and length of the shadow of a man are the same, then the angle of elevation of the Sun is 45°.
Reason : The value of tan 45° = 0.

Answer: C

Question. Assertion : Mohini looks at a top of tree and angle made is 45°. She moves 10 m back and again looks at the top of tree, but this time angle made is 30°, then height of the tree is (10√3 −1)m.
Reason : The angle of elevation and depression can be acute or obtuse angle.

Answer: C

Question. Assertion : The height of an observer is h m. He stands on a horizontal ground at a distance 3 h m from a vertical pillar of height 4h m. The angle of elevation of the top of the pillar as seen by the observer is 60°. 
Reason : The value of tan 60° = 3.

Answer: A

Question. Assertion : If a vertical tower of height 50 m casts a shadow of length 50 3 m, then the angle of elevation of the Sun is 60°.
Reason : If the angle of elevation of the Sun decreases, then the length of shadow of a tower increases.

Answer: D

Question. Assertion : A ladder 16 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is 8 m.
Reason : The value of sin 60° = √3/2

Answer: B