Trigonometry

A ladder rests against a vertical wall at angle α. If its foot is pulled distance 'a' so it makes angle β, the distance 'b' it slides down is:

A tower subtends an angle α at a point A and elevation of top of a flagstaff on it is β. If h is flagstaff height, tower height is:

Shadow of tower is 30m when elevation is 30°. When elevation is 60°, shadow is:

From top of tower h, elevation of a balloon is α and depression of its reflection is β. Height of balloon?

Angle of elevation of top of tower from a point A is α. Walking distance 'd' towards it, it is β. Height h is:

A flagstaff on a tower 20 m high subtends 45° at a point 20 m from the foot. Flagstaff height?

Angle of elevation of an object from a point 100 m high is 30°. If the object is 200 m from the base, find its height.

If the elevation of sun changes from 30 to 60, the shadow of a tower decreases by 10 m. Height?

Height of two towers are h1 and h2. If elevation of top of first from foot of second is 60 and vice versa is 30, h1/h2 is:

A man in a boat moving away from a cliff 100 m high takes 2 mins for elevation to change from 60 to 30. Speed?

Length of a shadow of a vertical tower on level ground increases by 10 m when altitude of sun changes from 45 to 30. Height?

The angle of elevation of the top of a tower from a point A due south is 30° and from B due east is 45°. If AB = 100 m, find height.

From top of building, depression of top and bottom of pole are 30 and 45. If pole is 10 m, building is:

A ladder leans against a wall at 60. If the foot is pulled 2 m, it makes 30. Ladder length?

Two people are on opposite sides of a tower 100 m high. Elevation is 30 and 60. Distance between them?

From a point on the ground, the angle of elevation of a jet plane is 60°. After a flight of 15 seconds, it becomes 30°. If plane flies at 1500√3 m, find speed.

The angle of elevation of the top of a tower from a point is α. On moving distance 'a' towards it, it is 45 and 'b' more, it is 90-α. Height?

An observer finds elevation of a hill top as 30. Moving 1 km towards it, it is 45. Hill height?

A balloon is at height 'h'. Angle of elevation from ground is α. It moves horizontally distance 'd' and elevation is β. Then d is:

Express tan θ in terms of sin θ and cos θ.