Page 1 :
GALACTIC INSTITUTE, , HARE, , KRISHNA, , MATHEMATICS-X-10-, , PRACTICE EXERCISE 9.1, Q.1 A tower is 100√3 metres high. Find the angle of elevation if its top from a, point 100 metres away from its foot., Ans.θ=60°, Q.2 A vertical tower stands on a horizontal plane and is surmounted by a, vertical flagstaff of height h.Ata point on the plane, the angles of elevation of, the bottom and the top of the flag-staff are α and β respectively. Prove that the, height of the tower is [HOTS], –, , Ans. The height of the tower is, Q.3 A tree 12 m high, is broken by the wind in such a way that its top touches, the ground and makes an angle 60° with the ground. At what height from the, bottom the tree is broken by the wind?, Ans. The tree is broken at a height of 5.569 metres from the ground., Q.4 From the top of a building 60 m high the angles of depression of the top, and the bottom of a tower are observed to be 30° and 60°. Find the height of, the tower., [CBSE 2005], Ans.The height of the tower is 40 metres., Q.5 The angle of elevation of a jet plane from a point A on the ground is, 60°.After a flight of 30 seconds, the angle of elevation changes to 30°. If the jet, plane is flying at a constant height of 3600√3 m, find the speed of the jet, plane., [CBSE 2008, 2014], Ans. The height of the tree is 36.6 m., Q.6 The angle of elevation of a cliff from a fixed point is θ. After going up a, distance of k metres towards the top of the cliff at an angle of Φ, it is found, that the angle of elevation is α. Show that the height of the cliff is, (, ), metres, [HOTS], –, , GALACTIC INSTITUTE : D-94/49 SECOND FLOOR, MAHAVIR ENCLAVE PART-II NEW DELHI Mob.8826181724, , Page 1

Page 2 :
GALACTIC INSTITUTE, , HARE, , KRISHNA, , MATHEMATICS-X-10-, , Q.7 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, Ans √3 + 1 𝑥, Q.8 From the top of a building 15 m high the angle of elevation of the top of a, tower is found to be 30°. From the bottom of the same building, the angle of, elevation of the top of the tower is found to be 60°. Find the height of the, tower and the distance between the tower and building., Ans. Height = 22.5 m, Distance = 12.975 m, Q.9 The angle of elevation of an aeroplane from a point on the ground is 45°., After a flight of 15 seconds, the elevation changes to 30°. If the aeroplane is, flying at a height of 3000 metres, find the speed of the aeroplane., Ans. 527.04 km/hr, Q.10 The angles 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. Prove that the height of the tower is √ab metres., [HOTS] [CBSE 2002 C, 2004], Ans. The height of the tower is √ab metres, Q.11 A man standing on the deck of a ship, which is 10 m above water level, lie, 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°. Calculate the distance of the hill from, the ship and the height of the hill., [CBSE 2004, 2005, 2010], Ans. The distance of the hill from the ship is 10√3 metres and the height of the, hill is 40metres., , “Always keep in mind you are unique- just like every body else”, , GALACTIC INSTITUTE : D-94/49 SECOND FLOOR, MAHAVIR ENCLAVE PART-II NEW DELHI Mob.8826181724, , Page 2