Question

From a point on the ground 47ft from the base of a tree, the angle

of elevation to the top of the tree is 35 degrees. Find the height
of the tree to the nearest foot.

Answer 1

33 ft

Explanation:

In a diagram of the geometry, you see that the angle of elevation is opposite the triangle leg representing the tree height, and is adjacent to the triangle leg representing distance from the tree.

The tangent ratio relates these lengths to the angle:

Tan = Opposite/Adjacent

Opposite = Adjacent×Tan

tree height = (47 ft)tan(35°) ≈ 33 ft

The height of the tree is about 33 feet.