Question

Sarah walks 20 feet away from her house and places a mirror on the ground. She backs 5 feet away from the mirror so that she can see the tip of the roof. Sarah's eyes are 4 feet above the ground. Sarah and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Sarah's eyes, the mirror, and the ground are congruent as shown in the image below:

Image depicts a mirror on the ground between a person and a house. The mirror is 5 feet away from the person and 20 feet away from the house.

What is the height of the house? Show your work and explain your reasoning in complete sentences.

Answer 1

16 feet

Explanation:

As said in the problem statement, the angles between the top of the house, the mirror, and the ground and between Sarah's eyes, the mirror, and the ground are congruent.

We also know that Sarah and the house are perpendicular to the ground.

So if we draw a triangle from the top of the house, to the mirror, to the bottom of the house, and another triangle from Sarah's eyes, to the mirror, to Sarah's feet, we get two triangles that have the same angles. Therefore, the triangles are similar, and we can write a proportion:

4 / 5 = h / 20

h = 16

The house is 16 feet tall.