Question

For a project in his Geometry class, Ryan uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.15 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. He then walks 3.4 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

Answer 1

9514 1404 393

Answer:

4.82 m

Explanation:

The mirror reflects light at the same angle the light hits it, so the triangles formed by the line of sight, the ground, and the objects involved are similar. This means corresponding lengths are proportional.

height/mirror distance = T/12.15 = 1.35/3.4

Multiplying by 12.15, we find the top of the goalpost to have a height of ...

T = 12.15(1.35/3.4) ≈ 4.82 . . . meters

The goalpost is about 4.82 meters high.