Question

for a project in his geometry class, elijah uses a mirror on the ground to measure the height of his school building. he walks a distance of 8.25 meters from the school, then places a mirror flat on the ground, marked with an x at the center. he then steps 0.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the x. his partner measures the distance from his eyes to the ground to be 1.45 meters. how tall is the school? round your answer to the nearest hundredth of a meter. (diagram is not to scale.) answer attempt 1 out of 2

Explanation:

Step1: Set up proportion

By the law of reflection and similar - triangles, the ratio of the height to the base of the two similar right - triangles is equal. Let $h$ be the height of the school. The two similar right - triangles are formed by the person's height and distance from the mirror, and the school's height and its distance from the mirror. So we have the proportion $\frac{h}{8.25}=\frac{1.45}{0.8}$.

Step2: Solve for $h$

Cross - multiply the proportion: $h=\frac{1.45\times8.25}{0.8}$. First, calculate $1.45\times8.25 = 1.45\times(8 + 0.25)=1.45\times8+1.45\times0.25=11.6 + 0.3625 = 11.9625$. Then, $h=\frac{11.9625}{0.8}=14.953125$.

Step3: Round the answer

Rounding $14.953125$ to the nearest hundredth, we get $h\approx14.95$.

Answer:

$14.95$ meters