Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 55∘. How tall is the tree if the point on the ground is 90 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

Let h be the tree height. Using tan(55°) = opposite/adjacent = h/90,

h = 90·tan(55°) ≈ 90·1.428148 = 128.53 feet.

So the tree is about 128.53 ft tall (to the nearest hundredth).