For a project in her Geometry class, Addison uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.25 meters from the goalpost, then places a mirror on 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 1.55 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

Question

For a project in her Geometry class, Addison uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.25 meters from the goalpost, then places a mirror on 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 1.55 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

Answer 1

Let's call the height of the goalpost "x".

Based on the given information, we can create a right triangle. The mirror serves as one leg of the triangle, while Addison's distance from the mirror to the goalpost serves as the other leg.

Using the Pythagorean theorem, we have:
x^2 = (13.25 + 1.3)^2 - 1.55^2
x^2 = (14.55)^2 - 2.4025
x^2 = 211.68025 - 2.4025
x^2 = 209.27775

Taking the square root of both sides:
x = √209.27775
x ≈ 14.47

Therefore, the height of the goalpost is approximately 14.47 meters.