Questions: Keiko wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 34 ft from the tree, and Keiko is standing 9.8 ft from the mirror, as shown in the figure. Her eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot. The figure is not drawn to scale.

Solution Steps

The triangles formed by Kelko and the mirror and the tree and the mirror are similar triangles. Therefore, the ratio of corresponding sides is equal. We can set up a proportion:

height of tree / distance from tree to mirror = height of Kelko / distance from Kelko to mirror

Let _h_ represent the height of the tree.

_h_ / 34.8 ft = 6 ft / 9.8 ft

Cross-multiply:

9.8 * _h_ = 34.8 * 6

9.8_h_ = 208.8

Divide both sides by 9.8:

_h_ = 208.8 / 9.8

_h_ ≈ 21.31 ft

Rounding to the nearest foot, we get 21 ft.

Final Answer