Question

for a project in her geometry class, scarlett uses a mirror on the ground to measure the height of her school building. she walks a distance of 11.25 meters from the school, then places a mirror flat on the ground, marked with an x at the center. she then steps 0.9 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 1.55 meters. how tall is the school? round your answer to the nearest hundredth of a meter.

Explanation:

Step1: Identify similar triangles

The two triangles (Scarlett's height - mirror distance and school height - school - mirror distance) are similar, so their ratios are equal. Let \( h \) be the school's height. Then \(\frac{h}{11.25}=\frac{1.55}{0.9}\).

Step2: Solve for \( h \)

Multiply both sides by 11.25: \( h = \frac{1.55\times11.25}{0.9} \).
Calculate numerator: \( 1.55\times11.25 = 17.4375 \).
Divide by 0.9: \( h=\frac{17.4375}{0.9}=19.375 \).
Round to nearest hundredth: \( h\approx19.38 \).

Answer:

19.38 meters