Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 64∘. How tall is the tree if the point on the ground is 26 feet from the bottom of the tree? Round your answer to the nearest tenth of a foot if necessary.

Answer 1

Let h be the tree height. Then tan(64°) = h/26, so h = 26·tan(64°) ≈ 26·2.0516 ≈ 53.3 feet.

The tree is about 53.3 ft tall.