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. 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:

Part 1: Prove the triangles are similar.
Part 2: Determine the height of the house.

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. 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:

Part 1: Prove the triangles are similar.
Part 2: Determine the height of the house.

anonymous · Answer

attachment

anonymous · Answer

@campbell_st @primeralph

campbell_st · Answer

well looking at the information the angle between the ground and Sarah is a right angle and so is the angle between the house wall and th ground. 

so the triangles are similar by Angle Angle Postulate

the to find the height of the house use ratios of corresponding sides... 

$$\frac{20}{5} = \frac{h}{4}$$

anonymous · Answer

Where did you get those numbers from?

campbell_st · Answer

from the question.... 

and you use the corresponding sides

anonymous · Answer

Oh okay. I didn't realize that's what you did

anonymous · Answer

I got 16 for the height of the house. Thank you