Annie walks 15 feet away from her house and places a mirror on the ground. She backs 4 feet away from the mirror so that she can see the tip of the roof. Annie's eyes are 5 feet above the ground. Annie and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Annie'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 4 feet away from the person and 15 feet away f


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

Answer:

The house is 18.75 feet tall

Step-by-step explanation:

The triangles are similar by the AA postulate.  

We are given the length of the bottom sides of the triangles, 4 and 15 respectively.  

Thus, the ratio is 4:15

We are also given the height of Annie's eyes, which is 5 feet. The height of the side that corresponds to the house is 5, so we can set up a proportion.

[tex]\frac{4}{15} = \frac{5}{x} \\4x = (5*15) = 75\\x = \frac{74}{4} \\x = 18.75[/tex]

Thus, the house is 18.75 feet tall.

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B
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