Question

question 8 of 10

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. 39 feet
c. 56 feet
d. 36 feet

Explanation:

Identify the given values and geometric setup

Using the Similar Right Triangles knowledge point

• Distance from tree base to mirror: \(d_1 = 42\text{ ft}\)
• Distance from Jason to mirror: \(d_2 = 7\text{ ft}\)
• Jason's eye height: \(h_2 = 6\text{ ft}\)
• Tree height: \(h_1\) (target unknown)

Set up the similarity proportion

Using the Similar Right Triangles knowledge point

$$ \frac{h_1}{d_1} = \frac{h_2}{d_2} $$

Solve for the tree height

Using the Similar Right Triangles knowledge point

$$
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$$

Answer:

• A. 49 feet
• B. 39 feet
• C. 56 feet
• D. 36 feet (Correct answer)