From the top of the tower of 24 meter height, a man observes a child playing on the ground at an angle of depression of 30°. After sometimes, he observed that the angle of depression is 60°. Find the distance covered by kid.

In a triangle ABC right angled at B, AB=8 unit and AC=10 unit. What is the value of $\sin^2\theta - \cos^2\theta$ where theta is angle ACB ?

If the height of tree is $3\sqrt{3}$ meters and length of its shadow is 3 meters. Find the angle of elevation of the sun.

The cliff of a mountain is 180 m high, and the angles of depression of two ships on the same side of cliff are 30° and 60°. Find the distance between the two ships in meter.

From a point P on the ground the angle of elevation of the top of 10 m high building is $30°$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from the point P is $45°$. Length of the flagstaff is:

(Take $\sqrt{3} = 1.732$)

In a $\Delta ABC$ right angled at A, if $\angle ABC = 60^\circ$ and AC = 4 units, then length of BC (in units) is :

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.