Question

ryan places a mirror on the ground 42 feet from the base of a tree. he walks backwards until he can see the top of the tree in the middle of the mirror. at that point, jasons eyes are 6 feet above the ground and he is 7 feet from the image in the mirror. what is the height of the tree?

a. 49 feet
b. 36 feet
c. 39 feet
d. 56 feet

Explanation:

Step1: Set up proportion

Since the angles of incidence and reflection are equal, we have similar right - triangles. Let $h$ be the height of the tree. The ratio of the height to the base of the triangle formed by the person is the same as the ratio of the height to the base of the triangle formed by the tree. So, $\frac{h}{42}=\frac{6}{7}$.

Step2: Solve for $h$

Cross - multiply: $7h = 42\times6$. Then $7h=252$. Divide both sides by 7: $h=\frac{252}{7}=36$.

Answer:

B. 36 feet