Question

Katie measures the angle of elevation from the ground to the top of an 18-foot-tall tree as 27°. To the nearest tenth of a foot, how far is she from the tree?

Answer 1

35.3 ft

Explanation:

You want the distance to a tree 18 ft high if the angle of elevation is 27°.

Tangent

The tangent of an acute angle in a right triangle is given by the ratio ...

Tangent = Opposite/Adjacent

Application

In this geometry, the values are ...

tan(27°) = (18 ft)/(distance to tree)

Solving for the distance to the tree, we have ...

distance to tree = (18 ft)/tan(27°) ≈ (18 ft)/0.50953 ≈ 35.3 ft

Katie is about 35.3 feet from the tree.