Application of Trigonometry (hots) question class -Xth
Some Applications of Trigonometry Questions
You are watching this hots questions
on Educbse (The platform of learning)
1. A person is standing on the bank of river, observes that the angle substended by a tree on the opposite bank is 60°. When he retreats 20m from the bank ,he finds the angle to be 30°. Find the height of the tree and the breadth of the river .
2. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane,the angle of elevation of the bottom and the top of the flag staff are alpha and beta respectively. Prove that the height of the tower is:-
h tan alpha /tan beta -tan alpha
3. A tree 12 m high ,is broken by the wind in such a way that it's 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?
4. The angles of elevation of the top of a tower from two points at a distance 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.
5. At a point on level ground,the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192 metres towards the tower ,the tangent of the angle of elevation is 3/4 . Find the height of the tower.
You are watching this hots questions on Educbse (The platform of learning)
6. The Shadow of a vertical tower on 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 to one place of decimal.
Take √3= 1.73
7. From the top of a hill,the angle of depression of two consecutive kilometre stones due to east are found to be 30° and 45°. Find the height of the hill.
8. Determine the height of the mountain if the elevation of its top at an unknown distance from the base is 30° and at a distance when kilometre further off from the mountain, along the same line, the angle of elevation is 15°.
Use tan 15°= 0.27
9. Two stations due south of a leaning tower which links towards the north are at distance a and b from its foot. If alpha ,beta be the elevations of the top of the tower from these stations, prove that its installation ∅ to the horizontal is given by
cot∅= b cot alpha - a cot beta/b - a
10. An aeroplane at an altitude of 1200 metres finds that two ships are sailing towards it in the same direction. The angles of depression of the ships as observed from the aeroplane are 60°and 30° respectively. Find the distance between two ships.
11. A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the tower ? Give your answer to the nearest second.
Take √3= 1.732
13.From the top of a building 60m high the angle of depression of the top and bottom of a tower observed to be 30° and 60°. Find the height of the tower.
14. A man standing on the deck of a ship, which is 10 metre above water level. He 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 help from the ship and the height of the hill.
You are watching this hots questions on Educbse (The platform of learning)
16. If the angle of elevation of a cloud from a point h metres above a lake is alpha and the angle of depression of its reflection in the lake is beta, prove that the height of the cloud is:-
h( tan beta + tan alpha )/ tan beta - tan alpha
17. The angle of elevation of a cloud from a point 60m above a lake is 30° and the angle of depression of the reflection of cloud and the lake is 60° . Find the height of the cloud.
18. There is a small island in the middle of a 100 metre wide river and a tall tree stands on the island. P and Q are points directly opposite to each other on two banks and in line with the tree. If the angle of elevation of the top of the tree from P and Q are respectively 30° and 45°, find the height of the tree .
19. The horizontal distance between two tower is 140 metre. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30° . If the height of the second tower is 60 metre, find the height of the first tower.
20. A straight highway leads to the foot of a tower. A man is standing at the top of a tower observes a car at an angle of depression of 30°, which is approaching to the foot of the tower with the uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the further time taken by the car to read the foot of the tower.
You are watching this hots questions on Educbse (The platform of learning)
Thank you very much
By Anuranjan Gadekar
No comments