Some Applications Of Trigonometry Class 10
Some Applications Of Trigonometry Class 10
CH – 9 SOME APPLICATIONS OF TRIGONOMETRY
1. The length of shadow of a tower on the plane ground is √3 times the height of the tower. The angle of elevation of sun is
a) 450 b) 300 c) 600 d) 900
2. The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 300. The distance of the car from the base of the tower ( in metres) is
a) 25√3 b) 50 √3 c) 75 √3 d) 150
3. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 600 with the wall, then the height of the wall is ____ m
a) 15√3 b) 15√3 /2 c) 15/ 2 d) 15
4. If a pole 6 m high casts a shadow 2√3 m long on the ground, then sun’s elevation is _____ degrees
a) 60 b) 45 c) 30 d) 90
5. Two friends Rohit and Mohit are standing on the opposite sides of a tower of height 60 m. If their angles of depression seen from the top of the tower are 30 and 45 degrees respectively, then the distance between the two friends is ____ m
a) 60 (√3 – 1) b) 60 (√3 + 1) c) 30 (√3 – 1) d) 30 (√3 + 1)
6. The ratio of the height of a tower and the length of its shadow on the ground is
7. The tops of two towers of height x and y, standing on level ground, subtend angles of 300 and 600 respectively at the centre of the line joining their feet, then find x : y
8. A boy standing on a horizontal plane finds a bird flying at a distance of 100m from
him at an elevation of 30o. A girl standing on the roof of 20m high building find the
angle of elevation of the same bird to be 45o.Both the boy and girl are on opposite
sides of the bird. Find the distance of the bird from the girl.
9. 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)
10. 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.
11. 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.
12. 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.
13. A ladder set against a wall at an angle 450 to the ground. If the foot of the ladder is pulled away from the wall through a distance of 4 m, its top slides a distance of 3 m down the wall making an angle 300 with the ground. Find the final height of the top of ladder from the ground and length of the ladder.
13. 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)
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. An aeroplane flying horizontally at a height of 2500 m above the ground is observed at an elevation of 600 and after 15 sec, the elevation is observed to be 300. Find the speed (in km/h) of the aeroplane.
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Some Applications Of Trigonometry Class 10
Some Applications Of Trigonometry Class 10
Some Applications Of Trigonometry Class 10
Some Applications Of Trigonometry Class 10
Some Applications Of Trigonometry Class 10