(05.03 MC) Paul walks 25 feet away from his house and places a mirror on the ground. He backs 5 feet away from the mirror so that he can see the tip of the roof. Paul's eyes are 6 feet above the ground. Paul and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Paul's eyes, the mirror, and the ground are congruent as shown in the image below:

What is the height of the house? Show your work and explain your reasoning in complete sentences. (10 points)

looks like you have 2 similar triangles.

all the angles from one triangle are congruent to all the angles from the other triangle.

the sides must be proportional.

therefore 6/5 = x/25, where x is the height of the house, 6 is the height of paul's eyes, 5 is the distance between paul and the mirror, and 25 is the distance between the house and the mirror.

cross mltiplyh to get 6*25 = 5*x

divide both sides of the equation by 5 to solve for x to get:

x = 6*25/5 = 6*5 = 30.

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hope this helps

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