Question

for a project in her geometry class, kylie uses a mirror on the ground to measure the height of her school’s football goalpost. she walks a distance of 13.55 meters from the goalpost, 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 goalpost clearly marked in the x. her partner measures the distance from her eyes to the ground to be 1.55 meters. how tall is the goalpost? round your answer to the n

Explanation:

Step1: Set up proportion

Since the two right - angled triangles formed are similar, the ratios of their corresponding sides are equal. Let $h$ be the height of the goalpost. The proportion is $\frac{h}{13.55}=\frac{1.55}{1.25}$.

Step2: Solve for $h$

Cross - multiply to get $h=\frac{1.55\times13.55}{1.25}$.
First, calculate $1.55\times13.55 = 20.9025$.
Then, $h=\frac{20.9025}{1.25}=16.722$.

Answer:

$16.72$ (rounded to two decimal places)