From the top of a lighthouse, 100 m high, the angle of depression of a boat is $${\tan ^{ - 1}}\left( {{5 \over {12}}} \right)$$. What is the distance between the boat and the lighthouse?

A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is 48$$^\circ$$. If the height of the balloon above the bridge is 122m, then what is the length of the bridge?

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation $${\pi \over 6}$$ and $${\pi \over 3}$$ respectively. What is the height of the hill?

If a flage-staff of 6m height placed on the top of a tower throws a shadow of $$2\sqrt 3 $$ m along the ground, then what is the angle that the sun makes with the ground?