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, point, 4, 511.45 meters from the school, then places a mirror flat on the ground, marked with an X at the center. She then steps 1, point, 2, 51.25 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, point, 1, 51.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.

Answer 1

Use similar triangles: height H of the school and eye height h satisfy H / (distance school→mirror) = h / (distance eyes→mirror). So

H = h * (distance school→mirror) / (distance eyes→mirror).

With the given numbers (distance school→mirror = 11.451145 m, distance eyes→mirror = 1.25125 m, eye height h = 1.15115 m),

H = 1.15115 * (11.451145 / 1.25125)
≈ 1.15115 * 9.151764235
≈ 10.535053399

Rounded to the nearest hundredth: 10.54 m.