Questions in trigonometry

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From a 60 meter high tower angles of depression of the top and bottom of a house are $\alpha$ and $\beta$ respectively. If the height of the house is $\frac{60\,\sin \,(\beta -\alpha )}{x},$ then $x =$
An observer on the top of a tree, finds the angle of depression of a car moving towards the tree to be 30°. After 3 minutes this angle becomes 60°. After how much more time, the car will reach the tree
A house of height 100 metres subtends a right angle at the window of an opposite house. If the height of the window be 64 metres, then the distance between the two houses is
The length of the shadow of a pole inclined at 10° to the vertical towards the sun is 2.05 metres, when the elevation of the sun is 38°. The length of the pole is
The angle of elevation of the top of a tower from a point 20 metre away from its base is 45°. The height of the tower is
The horizontal distance between two towers is 60 metres and the angular depression of the top of the first tower as seen from the top of the second, is 30°. If the height of the second tower be 150 metres, then the height of the first tower is
From the top of a light house 60 meters high with its base at the sea level, the angle of depression of a boat is 15°. The distance of the boat from the foot of light house is
An observer in a boat finds that the angle of elevation of a tower standing on the top of a cliff is 60° and that of the top of cliff is 30°. If the height of the tower be 60 meters, then the height of the cliff is
A tower subtends an angle $\alpha$ at a point A in the plane of its base and the angle of depression of the foot of the tower at a point l meters just above A is $\beta$. The height of the tower is
The angle of elevation of a tower from a point A due south of it is 30° and from a point B due west of it is 45°. If the height of the tower be 100 metres, then AB =

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