CBSE Class 10 Mathematics Applications Of Trigonometry Worksheet Set G

Question. A 1.6 m tall girl stands at a distance of 3.2m from a lamp post and casts a shadow of 4.8 m on the ground. Find the height of the lamp post
Answer : (2.6m)

Question. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill is 60˚ and the angle of depression of the base of the hill is 30.˚ Calculate the distance of the hill from the ship and the height of the hill
Answer : (10√3m, 40m)

Question. The angle of elevation of a cloud from a point 60m above a lake is 30˚ and angle of depression of the reflection of cloud in the Lake is 60˚. Find the height of the cloud.
Answer : (120 m)

Question. The angle of elevation of a jet plane from a point A on the ground is 60˚. After a flight of 15 sec the angle of elevation changes to 30˚. If the jet plane is flying at a constant height of 1500√3m, then find the speed of jet plane.
Answer : (720 km /hr)

Question. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angles of elevation at the bottom and the top of the flagstaff are α and β respectively.
Answer : Prove that the height of the tower is h tan α / tanβ – tanα

Question. The angle of elevation of the top of a tower from two points at distances a and b metres from the base and in the same straight line with it are complementary.
Answer : Prove that height of the tower is √ab metres.

Question. The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are 30˚ and 45˚respectively. Find the height of the rock.
Answer : (236.5 m)

Question. A boy is standing on the ground and is flying a kite with 100m of string at an elevation of 30˚ Another boy is standing on the roof of a 10m high building and is flying his kite at an elevation of 45˚. Both the boys are on opposite sides of the kite’s .Find the length of the string that the Second boy must have so that two kites meet.
Answer : (40√2 m)

Question. the shadow of a tower standing on a level ground is found to be 40 m longer when the sun, s altitude is 30˚ than when it is 60˚. Find the height of the tower.
Answer : (20√3m)

Question. The angle of elevation ø of a vertical tower from a point on ground is such that its tangent is 5/12. On walking 192m towards the tower in the same straight line, the tangent of the angle of elevation Is found to be ¾. Find the height of the tower
Answer : (180 m)

Question. A bird is sitting on the top of a tree, which is 80m 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 sec, the angle of Elevation of the bird from the point of observation becomes 30˚. Find the speed of flying of the bird
Answer : (29.28m/sec)

Question. An aero plane at an altitude of 200m observes the angles of depression of opposite points on the two banks of a river to be 45˚ and 60˚. Find the width of the river
Answer : (315.4m)

Question. Two men on either side of a cliff, 60m high, observe the angles of elevation of the top of the cliff to be 45˚ and 60˚ respectively Find the distance between two men
Answer : (94.6m)