A lamp post is situated at the middle point M of the side AC of a triangular plot ABC with BC=7m, CA=8m, AB=9m. Lamp post subtends an angle `15^@` at the point B. Determine the height of the lamp post.

A tree breaks due to a strom and the broken part bends so that the top of the tree touches the ground making an angle 30 with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree.

A tree stands vertically on a hill side which makes an angle of 15^@ with the horizontal. From a point on the ground 35m down the hill from the base of the tree, the angle of elevation of the top of the tree is 60^@ . Find the height of the tree.