Question

For a project in his Geometry class, Yusuf uses a mirror on the ground to measure the height of his

school building. He walks a distance of 10.25 meters from the building, then places a mirror flat on the
ground, marked with an X at the center. He then walks 1.65 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

Using similar triangles, the height of the school building is approximately 11.12 meters when calculated from the given measurements of distances and Yusuf's eye level to the ground.

Step-by-step explanation:

To determine the height of the school building that Yusuf is measuring, we can apply similar triangles since the light follows a straight path.

Yusuf's line of sight to the top of the building when looking into the mirror forms a right triangle with the mirror and the building.

The distance Yusuf walked beyond the mirror (1.65 meters) and the height from his eyes to the ground (1.55 meters) form one triangle, while the entire distance from the mirror to the building (10.25 + 1.65 = 11.90 meters) and the building's height form another triangle.

Step by Step Solution:

• Yusuf's eye level to the ground is 1.55 meters.

• Distance from the mirror to where Yusuf's eye level meets the reflection is 1.65 meters.

• Total distance from the building to the mirror is 10.25 + 1.65 = 11.90 meters.

• The triangles are similar, so the ratios of corresponding sides are equal. This gives us the proportion (Building Height / 11.90) = (1.55 / 1.65).

Solving this proportion for the Building Height yields Building

Height = (1.55 / 1.65) * 11.90.

Calculating the value gives us Building: Height ≈ 11.118 meters (rounded to the nearest hundredth).

Therefore, the height of the school building is approximately 11.12 meters.