Question

1. mr. childress decided that he wanted to know the height of the statue of liberty. he placed a mirror on the ground 152.5 feet from the base of the statue. he then walked backwards until he could see only the very top of the monument in the mirror. he was 3 feet from the mirror at this point. using similar triangles, how tall is the statue of liberty?

x =
feet tall

Explanation:

Step1: Identify similar triangles

The two right triangles (one formed by the person and their distance from the mirror, the other by the statue and its distance from the mirror) are similar by the AA (Angle - Angle) similarity criterion (both have a right angle and share the angle of incidence/reflection). So, the ratios of corresponding sides are equal.
Let the height of the statue be \( x \) feet. The ratio of the person's height to their distance from the mirror should equal the ratio of the statue's height to its distance from the mirror. The person's height is 6 feet, distance from mirror is 3 feet, statue's distance from mirror is 152.5 feet. So we set up the proportion: \(\frac{6}{3}=\frac{x}{152.5}\)

Step2: Solve the proportion

Cross - multiply: \( 3x=6\times152.5 \)
First, calculate \( 6\times152.5 = 915 \)
Then, divide both sides by 3: \( x=\frac{915}{3}=305 \)

Answer:

305