Important questions of Maths class 10 chapter 9
CLASS- X
Session 2022-23
CH – 9. SOME APPLICATIONS OF TRIGONOMETRY
1. The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1 . What is the angle of elevation of the sun?
2. A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 30⁰. A girl standing on the roof of 20m high building find the angle of elevation of the same bird to be 45⁰.Both the boy and girl are on opposite sides of the bird. Find the distance of the bird from the girl.
3. A man rowing a motorboat away from a lighthouse 150 m high takes 2 minutes to change the angle of elevation of the top of lighthouse from 45⁰ to 30⁰. Find the speed of the boat. ( use √3 = 1.732)
4. The angle of elevation of a cloud from a point 60m above a lake is 30 degree, and the angle of depression of the reflection of the cloud in the lake is 60 degree. Find the height of the cloud from the surface of the lake.
5. From a point P on the ground, the angle of elevation of the top of a 10 m tall building and a helicopter, hovering at some height vertically over the top of the building are 30⁰ and 60⁰ respectively. Find the height of the helicopter above the ground.
6. The angle of elevation of the top of a hill at the foot of a tower is 60⁰ and the angle of depression from the top of a tower to the foot of hill is 30⁰.If tower is 50 m high, find height of the hill.
7. A pole 5 metre high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60⁰ and the angle of depression of the point A from the top of the tower is 45⁰.Find the height of the tower.(use √3=1.73)
8. The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the sun is 60⁰. Find the angle of elevation of the sun of the longer shadow.
9. A bird is sitting on the top of a tree ,which is 80 m high . The angle of elevation of the bird, from a point on the ground is 45⁰. The bird flies away from the point of observation horizontally and remains at a constant height .After 2 seconds; the angle of elevation of the bird from the point of observation becomes 30 degree. Find the speed of the flying of the bird.
10. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 30⁰ and 60⁰ respectively. Find the distance between the two planes at that instant.
11. The angle of elevation of the top of a vertical tower from a point on the ground is 60⁰.From another point 10 m vertically above the first ,its angle of elevation is 30⁰.Fjnd the height of the tower.
12.Two poles are 25 metre and 15 metre high and the line joining their tops makes an angle of 45⁰ with the horizontal. Determine the distance between these poles.
13. A man on the deck of a ship, 12m above water level, observes that the angle of elevation of the top of the cliff is 60⁰ and the angle of depression of the base of the cliff is 30⁰. Find the distance of the cliff from the ship and the height of the cliff.
14. A vertical pedestal stands on the ground and is surmounted by a vertical flagstaff of height 5m. At a point on the ground, the angles of elevation of the bottom and the top of the flagstaff are 30⁰ and 60⁰ respectively. Find the height of the pedestal.
15. From a window (9m above the ground) of a house in a street, the angles of elevation and depression of the top and foot of another house on the opposite side of the street are 30⁰ and 60⁰ respectively. Find the height of the house and the width of the street. [ Use √3= 1.732]
ANSWERS: 1. 60⁰. 2. 30√2m. 3. 0.915m/s. 4. 120m. 5. 30m 6. 150 m 7. 6.825m. 8. 60⁰ 9. 40(√3-1)m/s. 10. 6250m 11. 15m. 12. 10m 13. 48m, 12√3m. 14 2.5m 15. 12m , 5.196m
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Important questions of Maths class 10 chapter 9
Important questions of Maths class 10 chapter 9
Important questions of Maths class 10 chapter 9