10TH CBSE MATHS APPLICATIONS OF TRIGONOMETRY MCQS WITH ANSWERS

 Q.1 The angle of elevation of a ladder against a wall is 60° and the foot of the ladder is 9.6 m from the wall. Find the length of the ladder.

(A) 29.2 m (B) 19.2 m (C) 20 m (D) 16.9 m

Q.2 If a pole 6 m high casts a shadow  long on the ground, then the Sun's elevation is:

(A) 60° (B) 45° (C) 30° (D) 90° 

Q.3 If the angle of elevation of a tower from a distance of 100 m from its foot is 60°, then the height of the tower is :

(A) (B) (C) (D) 

Q.4 A person standing on the bank of a river and he observes that the angle subtended by a tree on the opposite bank is 60°, when he retreates 20 m from the bank, he finds the angle to be 30°. Find the height of the tree and the breadth of the river.

(A) 17 m, 10 m (B) 17.32 m, 10 m (C) 15 m, 5 m (D) 15 m,10 m

Q.5 A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30°.

(A) 15 m (B) 20 m (C) 17.5 m (D) 10 m 

Q.6 An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

(A) 30° (B) 45° (C) 60° (D) 90° 

Q.7 A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance of 30 metres from the root. Find the whole height of the tree.

(A)  m (B)  m (C)  m (D) m 

Q.8 The shadow of a tower standing on a level plane is found to be 50 m longer when Sun's elevation is 30° than when it is 60°. Find the height of the tower.

(A)  m (B)  m (C)  m (D) m

Q.1 The ratio of the length of a rod and its shadow is 1 : 1. The angle of elevations of the Sun is :

(A) 30° (B) 45° (C) 60° (D) 90°

 

Q.2 An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 45° with the horizontal through the foot of the pole, find the length of the wire.

(A) 14.1 m (B) 11.1 m (C) 16 m (D) 17.5 m

Q.3 A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from a point A on the ground is 60° and the angle of depression of the point A from the top of the tower is 45°. Find the height of the tower.

(A) (B) (C) (D)  

Q.4 The length of a string between a kite and a point on the ground is 90 metres. If the string makes an angle q with the ground level such that , how high is the kite? Assume that there is no slack in the string.

(A) 79.41 m (B) 89.41 m (C) 75.21 m (D) 69.41 m

Q.5 The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point 10 m vertically above the first, its angle of elevation is 45°. Find the height of the tower.

(A) (B) (C) (D)  

Q.6 The angles of elevation of the top of a tower at the top and the foot of a pole of height 10 m are 30° and 60° respectively. Find the height of the tower.

(A) 20 m (B) 15 m (C) 25 m (D) 10 m 

Q.7 A vertical tower to stands on a horizontal plane and is surmounted by a vertical flag staff of height 

5 meters. At point on the plane, the angle of elevation of the bottom and the top of the flag staff are respectively 30° and 60°. Find the height of tower.

(A) 2 m (B) 3.5 m (C) 2.5 m (D) 5 m

Q.8 The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 metres longer than when it is 60°. Find the height of the tower.

(A) 23.65 m (B) 26.5 m (C) 20.65 m (D) 15.60 m 

Q.1 A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Find the height of the cliff.

(A) m (B) m (C) m (D) m

Q.2 A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at 60° to the  horizontal.Find the lenght of the string to the nearest metre.

(A) 85 m (B) 87 m (C) 80 m (D) 95 m

Q.3 A boy standing on a horizontal plane find a bird flying  at a distance of 100 m from him at an elevation of 30°. A girl standing on the roof of 20 metre high building finds the angle of elevation of the same bird to be 45°. Both the boy and the girl are on opposite side of the bird. Find the distance of bird from the girl.

(A) (B) (C) (D)  

Q.4 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, find the height of the building .

(A)  m (B)  m (C) 20 m (D)  m  

Q.5 A man of 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?

(A) 16 minutes 23 seconds (B) 15 minutes 20 seconds

(C) 10 minutes 23 seconds (D) 20 minutes 15 seconds 

Q.6 As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. Determine the distances travelled by the ship during the period of observation.

(A) 75.2 m (B) 70.5 m (C) 73.2 m (D) 60 m 

Q.7 The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 30 second, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of m, find the speed of the jet plane.

(A) 800 km/h (B) 864 km/h (C) 664 km/h (D) 846 km/h

Q.8 The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake.

(A) 100 m (B) 90 m (C) 120 m (D) 60 m

Q.1 The shadow of a vertical tower on level ground increases by 10 metres, when the altitude of the sun changes from angle of elevation 45° to 30°. Find the height of the tower, correct to one place of decimal. (Take  = 1.73) 

Q.2 From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 30° and 45°. Find the height of the hill.

Q.3 There is a small island in the middle of 100 m wide river and a tall tree stands on the island. P and Q are points directly opposite to each other on two banks and in line with the tree. If the angles of elevation of the top of the tree from P and Q are respectively 30° and 45°, find the height of the tree.

Q.4 The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 60 m, find the height of the first tower. 

Q.5 From a balloon vertically above a straight road, the angle of depression of two cars at an instant are found to be 45° and 60°. If the cars are 100 m apart, find the heights of the balloon.

Q.6 If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is . 

Q.7 The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what is the height of the hill?

Q.8 A man on the deck of a ship, 12 m above water level, observes that the angle of elevation of the top of a cliff is 60° and the angle of depression of the base of the cliff is 30°. Find the distance of the cliff from the ship and the height of the cliff. [Use  = 1.732]

ANSWERS