Avery uses similar triangles to measure the height of the football goalpost using a mirror on the ground. The resulting calculation yields a goalpost height of approximately 16.28 meters.
In this geometry problem, Avery is using the principle of similar triangles to determine the height of her school's football goalpost. When she stands at a distance of 14.55 meters from the goalpost and places a mirror on the ground with an X at the center, she creates two right-angled triangles. One triangle consists of her line of sight to the top of the goalpost, the distance from her eyes to the mirror, and the distance from the mirror to the goalpost. The other triangle is formed by her height, the distance between her eyes and the ground, and the distance from the mirror to her eyes.
Let h be the height of the goalpost. By similar triangles, the ratio of the height of the goalpost to the distance from the mirror to the goalpost is equal to the ratio of her height to the distance from the mirror to her eyes.
![\[ (h)/(14.55) = (1.45)/(1.3) \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/q0gb5akqs64j00dwtt5gr4tlzibtzpjao6.png)
Now, solving for h , we find:
![\[ h = (14.55 * 1.45)/(1.3) \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/5cuclz1c3rxl4593zglp4bxs2ktouizhwv.png)
After performing the calculation, the height of the goalpost is approximately 16.28 meters.