Question

liberal arts mathematics 1 sem 2
4.3.3 quiz: similar right triangles
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. 94 feet
b. 69 feet
c. 42 feet
d. 54 feet

Explanation:

Step1: Identify similar triangles

The two right triangles (tree - mirror - ground and person - mirror - ground) are similar by the law of reflection (angle of incidence = angle of reflection), so their corresponding sides are proportional. Let \( h \) be the height of the tree. The ratio of height to distance from mirror should be equal for both. So, \(\frac{h}{63}=\frac{6}{9}\).

Step2: Solve for \( h \)

Cross - multiply: \( 9h = 63\times6 \). Calculate \( 63\times6 = 378 \). Then, \( h=\frac{378}{9}=42 \).

Answer:

C. 42 feet