Apine tree growing on a hillside makes a 75° angle with the hill. from a point 80 feet up the hill, the angle of elevation to the top of the tree is 62° and the angle of depression to the bottom of the tree is 23°. what is the height of the tree to the nearest foot?

First, you should know:
 1. The Sum Property of Triangles says that the sum of the internal angles of a triangle is 180°.
 2. The angle of elevation is the angle that forms the visual line with the horizontal line.
 3. The angle of depression is the angle below of the horizontal line.
 4. The Sine Rule says that A/Sin(a)=B/Sin(b)=C/Sin(c).

 Let's call:

 a=75° (angle that the pine tree makes with the hill).
 b= 62°+ 23°=85° (The sume of the angle of elevation to the top of the tree and the angle of depression to the bottom of the tree).
 c= 20° (180°= a+b+c, so c=180°- 75°- 85°=20°).

 To find the heigh of the pine tree to the nearest foot, you must apply The Sine Rule explained before:

 A/Sin(a)=B/Sin(b)

 A= 80 ft
 B=?
 a= 20°
 b=85°

 80/Sin(20°)=B/Sin(85°)
 B= (Sin(85°)x80)/Sin(20°)
 B=233.01 ft

 What is the height of the tree to the nearest foot?
 The height of the tree to the nearest foot is 233.01 ft.