Peter walks 30 feet away from his house and places a mirror on the ground. he backs 6 feet away from the mirror so that he can see the tip of the roof. peter's eyes are 5 feet above the ground. peter and the house are both perpendicular to the ground. the angles between the top of the house, the mirror, and the ground and between peter'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 6 feet away from the person and 30 feet away from the house.
what is the height of the house? show your work and explain your reasoning in complete sentences.