Question

question 9 of 10
jason places a mirror on the ground 40 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 8 feet from the image in the mirror. what is the height of the tree?
a. 46 feet
b. 32 feet
c. 30 feet
d. 53 feet

Explanation:

Step1: Set up proportion

Since the triangles formed are similar (by the law of reflection, the angles are equal), we can set up a proportion. Let \(h\) be the height of the tree. The proportion is \(\frac{h}{40}=\frac{6}{8}\).

Step2: Solve for \(h\)

Cross - multiply: \(8h = 40\times6\). Then \(8h=240\). Divide both sides by 8: \(h=\frac{240}{8}=30\).

Answer:

C. 30 feet