Application of trigonometry

Very important questions for class 10th Maths

    
                                     Height and distance

1. A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

2. A tower is 100√3  high.  find the angle of elevation of its top from a point 100 metres away from its foot

3. An electrician has to repair an electric fault on a pole of height 5 m. He needs to reach a point 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which, when inclined at an angle of 60° to the horizontal, would enable him to reach the required position? Also, how far from the foot of the pole should he place the foot of the ladder

4. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.


5. the angle of elevation of the top of a tower from a point on the same level as the foot of the tower 150 m towards the foot of the tower, the angle of elevation becomes 60°. Show that the height of the tower is 129.9 m.

6. The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the jet plane is flying at a constant height of 1500√3 m, find the speed of the jet plane.

7. Two pillars of equal heights stand on either side of a road which is 150 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60° and 30°. Find the height of each pillar and the position of the point on the road.

8. The angle of elevation of the top of a tower from two points on the ground at distances 'a' metres and 'b'  metres from the base of the tower and in the same straight line, are complementary. Prove that the height of the tower is √(ab) metres.

9. From a point on a bridge across a river, the angle of depression of the banks on opposite sides of river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.

10. An observed from the top of a Lighthouse 100 metre high above sea level the angle of depression of a ship sailing directly towards it changes from 30 degree to 60 degree determine the distance travelled by the ship during the period of observation

11. The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30 degree , if the tower is 50 m high,  find the height of the hill

12. A man standing on the Deck of ship which is 10 metre above the water level, observes the angle of elevation of the top of a hill 60 degree and the angle of depression of the base of the hill is 30 degree. Find the distance of the Hill from the ship and the height of the hill.

13. From a window 'h' metres high above the ground, of a house in a street, the angle 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 show that the height of the opposite house is h(1+ tanA cotB )



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