Question

charles places a mirror on the ground 63 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 9 feet from the image in the mirror. what is the height of the tree?
a. 69 feet
b. 54 feet
c. 42 feet
d. 94 feet

Explanation:

Step1: Set up proportion

The two right - angled triangles formed are similar. Let the height of the tree be $h$. The ratio of the height to the base of the smaller triangle (formed by the person) is equal to the ratio of the height to the base of the larger triangle (formed by the tree). So we have the proportion $\frac{h}{63}=\frac{6}{9}$.

Step2: Solve for $h$

Cross - multiply: $9h = 6\times63$. Then $9h=378$. Divide both sides by 9: $h=\frac{378}{9}=42$.

Answer:

C. 42 feet