Question

For a project in his Geometry class, Chase uses a mirror on the ground to measure the height of his school building. He walks a distance of 6.75 meters from the building, then places a mirror flat on the ground, marked with an X at the center. He then walks 3.45 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.55 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.

Answer 1

To find the height of the school building, we can use similar triangles formed by Chase's position and the mirror. By setting up a proportion with the similar triangles, we can solve for the height of the building.

Step-by-step explanation:

To calculate the height of the school building, we can use similar triangles formed by Chase's position and the mirror. Let's call the height of the school building 'h'.

Chase is 6.75 meters away from the building and his partner measures the distance from his eyes to the ground as 1.55 meters. When Chase walks 3.45 meters past the mirror, he can see the top of the school building in the mirror. This means that the height of the mirror from the ground is 1.55 + h. By setting up a proportion with the similar triangles, we can solve for h.

Using the proportion (h / (1.55 + h)) = (6.75 / 3.45), we can cross multiply and solve for h.

Simplifying the equation, h = (1.55 * 6.75) / (3.45 - 1.55).

Plugging in the values, we get h = 3.01 meters. Therefore, the height of the school building is approximately 3.01 meters.