A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite sides of the lane are found to be `alpha and beta` respectively. Prove that the height of the other house is `h(1 + tan alpha cot beta)` metres.

A bridge across a valley is h metres long. There is a temple in the valley directly below the bridge. The angles of depression of the top of the temple from the two ends of the bridge are alpha and beta . Prove that the height of the bridge above the top of the temple is (h (tan alpha tan beta))/(tan alpha + tan beta) metres.

A building stands on a horizontal plane and is surmounted by a vertical flag-stagg of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are alpha and beta respectively. Prove that the height of the building is (h tan alpha)/(tan beta-tan alpha)

If the angle of elevation of a cloud from a point h metres above the surface of a lake is alpha and the angle of depression of its reflexion in the lake is beta , prove that the height of the cloud is (h (tan beta + tan alpha))/(tan beta - tan alpha) metres.

A jet plane is at a vertical height of h. The angles of depression of two tanks on the ground in the same line with the plane are alpha and beta (alpha gt beta) . Prove that the distance between the tanks is ( h (tan alpha - tan beta))/(tan alpha tan beta)

The angle of elevation of the top of a tower from a point P on the ground is alpha . After walking a distance of d m towards the foot of the tower, the angle of elevation of the top of the tower is found to be beta . Then, ………..holds good.