A pine tree stands beside a road that has a 7 degree gradient. When the angle of elevation to the sun is 59 degrees, the tree casts a shadow of 31 ft down slope along the road. What is the height of the tree?

Answer 1

Draw a diagram.

If the tip of the shadow is x feet horizontally away from the tree of height x, we have

x/31 = cos 7°
(h + 31*sin7°)/x = tan 59°

I get h = 47.4 ft