Answer the following
1. If the angle of elevation of a tower from a distance of 100 m from its foot is 60° then find the height of the tower.
2. The height of a tower is 50 m. When angle of elevation changes from 45° to 30°, the shadow of tower becomes x metres more, then find the value of x
3. A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°
4. From a window (9m above 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 30°and 60° respectively. Find the height of the opposite house and width of the street.
5. Two poles of equal heights are standing opposite each other on either side of the road, which is 80m wide. From a point between them on the road the angles of elevation of the top of the poles are 60° and 30°. Find the heights of pole and the distance of the point from the poles.
6. A window in a building is at a height of 10m above the ground. The angle of depression of a point P on the ground from the window is 30°. The angle of elevation of the top of the building from the point P is 60° . Find the height of the building
7. Two ships are sailing in the sea on the either side of the light-house, the angles of depression of two ships as observed from the top of the light-house are 60° and 45° respectively. If the distance between the ships is 200 (root 3 +1)/root 3 metres, find the height of the light-house
8. The angles of elevation and depression of the top and bottom of a light-house from the top of a building 60 m high, are 30° and 60° respectively. Find
(i) the difference between the heights of the light-house and the building.
(ii) distance between the light-house and the building.
9. The angle of elevation of a jet fighter 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 is flying at a speed of 720 km/h. find the constant height at which the jet is flying.
10. A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an
elevation of 30°. A girl, standing on the root of 20m high building, finds the angle of elevation of the same bird to be 45°. Both the boy and girl are on the opposite sides of the bird. Find the distance of bird from the girl.
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