Question

A tree grows vertically on a hillside. The hill is at a 16° angle to the horizontal. The tree casts an 18-meter shadow up the hill when the angle of elevation of the sun measures
68°. How tall is the tree?

Answer 1

The height of the tree is the sum of the part below the line parallel to the horizontal and the part above the line parallel to the horizontal.

Height of the part below the line parallel to the horizontal = 18 sin16° = 4.96 meters
Horizontal distance of the tip of the of the shadow from the tree = 18 cos16° = 17.30 meters
Height of the part above the line parallel to the horizontal = 17.3 tan68° = 42.83 meters

Height of the tree = 4.96 + 42.83 = 47.79 meters