Q. 1. On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 600 and 300; respectively. Find the height of the tower and flagpole mounted on it.
Q. 2. Two walls are at a distance of 5m from each other. A ladder, kept resting on one wall; touch the wall at a point 6m above the ground. When moves towards the second wall, keeping the foot of the ladder fixed, touches the second wall 5m above the ground. Find the distance of the foot of the ladder from the first wall.
Q. 3. A vertical straight tree, 15m high, is broken by the wind in a such a way that its top just touches the ground and makes an angle of 60 with the ground .At what height from the ground did the tree break.
Q. 4. A tower is 50m high. Its shadow is x m shorter when the suns altitude is 450 and 360 respectively. Find the height of the tower correct to one place of decimal.
Q. 5. A bird is sitting on the top of a tree, which is 80m high. The angle of elevation of the bird, from a point on the ground is 450.The bird flies away horizontally and remains at a constant height. After 2 seconds, the angle of elevation of the bird from the point of observation becomes 300. Find the speed of flying of the bird.
Q. 6. The angle of elevation of a jet plane from a point P on the ground is 600.After a flight of 15 seconds, the angle of elevation changes to 300.If the jet plane is flying at a constant height of 1500 √ 3m, find the speed of the jet plane.
Q. 7. Two poles of height 7m and 12m stand on a plane ground. If the distance between their feet is 12m,find the distance between their tips.
Q. 8. A round balloon of radius r subtends an angle of α at the eye of the observer while the angle of elevation of its centre is β. Prove that the height of the centre of the balloon is rsin β cosec α/2.
Q. 9. From a window x metres high above the ground in a street, the angle of elevation and depression of the top and foot of the house on the opposite side of the street are α and β respectively. Show that the height of the opposite house is x (1+ tan α cot β ) metres.
