Q. 1. A man standing on the deck of the ship, which is 10 m above the water level, 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 hill from the ship and the height of the hill.
Q. 2. From a window x m high above the ground in a street, the angles of elevation and depression of the top and foot of the other house on the opposite side of the street are a and b resp. Show that the height of the house is 
Q. 3. Two pillars of equal heights stand on the either side of the roadway 150 m wide. From a point on the roadway between the pillars, the angles of elevation of the top of the pillars are 60° and 30°. Find the height of pillars and the position of the point.
Q. 4. On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 m away from the foot of the tower the angle elevation of the top and bottom of the flag pole are 60° and 30°. Find the heights of the tower and the flag pole mounted on it.
Q. 5. The angles of depression of the top and bottom of a tower, as seen from the top of a 100 m high cliff, are 30° and 60° respectively. Find the height of the tower.
Q. 6. A bird 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 45°. 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°. Find the speed of flying of the bird.
Q. 7. From an aeroplane vertically above a straight line horizontal plane, the angles of depression of two consecutive km stones on the opposite sides of the aeroplane are found to be a and b. Show that the height of the aeroplane is 
Q. 8. If the angle of elevation of a cloud from a point h metres above a lake is a and the angle of its refection in the lake is b, prove that the distance of the cloud from the point of observation is 
Q. 9. The angles of elevation and depression of the top and bottom of a light-house from the top of a building 60 m high, 30° and 60° respectively. Find
Q. 10. From a window 60 metres high above the ground of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are 60° and 45° respectively. Show that the height of the opposite house is 
Q. 11. The angles of elevation of the top of a tower, as seen from two points A and B situated in the same straight line and at distances a and b respectively from the foot of the tower, are complementary. Prove that the height of the tower is 
Q. 12. An aeroplane when 3000 metres high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the two planes.
