Heights & Distances (Class-X)
Assignment 1
1. The shadow of a vertical standing on a 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 up to one decimal place.
2. The angle of elevation of a jet plane from ground is 60°. After 15 seconds of flight, the angle of elevation of the plane changes to 30°. If the plane is flying at constant height of 1500 /3 m, find the speed of plane in km/hr.
3. The angles of elevation of the top of a tower from two points P and Q in the same straight line with the base and at a distance of a and b metres from the tower are complementary. Prove that the height of the tower is |/ab metres.
4. From a window (h metres high above the ground) of a house in the street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are A and B respectively. Prove that the height of the opposite house is h(1 + tanA.cotB)
5. If the angle of elevation of a cloud from a point h metres above the lake is a and the angle of depression of its reflection in the lake is b, prove that distance of the cloud from the point of observation is
2h sec a
tanb – tana
6. A person standing on the bank of a river, 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.
7. A boy is standing on ground and flying a kite with 150 m of string at an elevation of 30°. Another boy is standing on the roof of a 25 m high building and flying a kite at an elevation of 45°. Find the length of string required by the second boy so that the two kites just meet, if both the boys are on opposite side of the kites.
ANSWERS
