Question

word problems, similar triangles (level 1)
score: 2.5/4 penalty: 0.5 off
question
for a project in her geometry class, avery uses a mirror on the ground to measure the height of her school’s football goalpost. she walks a distance of 14.55 meters from the goalpost, then places a mirror flat on the ground, marked with an x at the center. she then steps 1.3 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 1.45 meters. how tall is the goalpost? round your answer to the nearest hundredth of a meter.

Explanation:

Step1: Set up proportion

The two right - angled triangles formed are similar. Let $h$ be the height of the goalpost. The ratio of the height to the base of one triangle is equal to the ratio of the height to the base of the other triangle. So we have the proportion $\frac{h}{14.55}=\frac{1.45}{1.3}$.

Step2: Solve for $h$

Cross - multiply to get $1.3h = 1.45\times14.55$. Then $h=\frac{1.45\times14.55}{1.3}$.
First, calculate $1.45\times14.55 = 21.0975$. Then $h=\frac{21.0975}{1.3}=16.228846\cdots$.

Step3: Round the answer

Rounding $16.228846\cdots$ to the nearest hundredth gives $h\approx16.23$.

Answer:

$16.23$