Question

for a project in her geometry class, aria uses a mirror on the ground to measure the height of her school building. she walks a distance of 11.45 meters from the school, then places a mirror flat on the ground, marked with an x at the center. she then steps 1.25 meters to the other side of the mirror, until she can see the top of the school clearly marked in the x. her partner measures the distance from her eyes to the ground to be 1.15 meters. how tall is the school? round your answer to the nearest hundredth of a meter.

Explanation:

Step1: Set up the proportion

Since the two triangles (formed by Aria and the mirror, and the school and the mirror) are similar, we can set up the proportion \(\frac{\text{height of Aria}}{\text{distance from Aria to mirror}}=\frac{\text{height of school}}{\text{distance from school to mirror}}\). Let \(h\) be the height of the school. So, \(\frac{1.15}{1.25}=\frac{h}{11.45}\).

Step2: Solve for \(h\)

Cross - multiply: \(1.25h = 1.15\times11.45\). First, calculate \(1.15\times11.45 = 13.1675\). Then, \(h=\frac{13.1675}{1.25}\).

Step3: Calculate the value of \(h\)

\(h=\frac{13.1675}{1.25}=10.534\).

Answer:

\(10.53\) meters