A pine tree growing on a hillside makes a 74 degree angle wi

A pine tree growing on a hillside makes a 74 degree angle with the hill. From a point 80 feet up the hill, the angle of elevation to the top of the free is 62 degree and the angle of depression to the bottom is 18 degree. Find, to the nearest tenth of a foot, the height of the tree. The height of the tree is about feet. (Round to the nearest tenth as needed)

Solution

The bottome right angle of triangle is 62 +18 = 80 deg

The bottom left angle = 74 deg

the third angle of triangle = 180 -74 -80 = 26 deg

Apply sine rule: 80/sin26 = ht of tree/sin80

ht of tree = 80*sin80/sin26 = 179.72 = 179.7 ft