Question

For a project in her Geometry class, Ai Mi uses a mirror on the ground to measure the height of her school building. She walks a distance of 7.95 meters from the building, then places a mirror flat on the ground, marked with an X at the center. She then walks 2.3 more meters past the mirror, so that when she turns around and looks down at the mirror, 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 1.15 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 using a mirror on the ground, we can set up a proportion using similar triangles. Solving the proportion gives us the height of the mirror, which is half the height of the school. Therefore, the height of the school building is approximately 3.98 meters.

Step-by-step explanation:

To find the height of the school, we can use similar triangles. First, we need to determine the distance between Ai Mi's eyes and the mirror.

Ai Mi walks a distance of 7.95 meters to reach the mirror, then an additional 2.3 meters past the mirror. So, the total distance between her eyes and the mirror is 7.95 + 2.3 = 10.25 meters.

We can set up a proportion between the actual height of the school and the height of the mirror. Let's represent the height of the mirror as 'h'. Using the similar triangles formed by Ai Mi's eyes, the mirror, and the school building, we have:

(h + 1.15) / h = 10.25 / 7.95

Now, we can solve for 'h' by cross multiplying and simplifying the equation:

7.95(h + 1.15) = 10.25h

7.95h + 9.1425 = 10.25h

9.1425 = 10.25h - 7.95h

9.1425 = 2.3h

h = 9.1425 / 2.3

h = 3.975

Therefore, the height of the school is approximately 3.98 meters.