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AJ walks 20 feet away from his house and places a mirror on the ground. AJ backs 5 feet away from the mirror so that he can see the tip of the roof. AJ's eyes are 5.5 feet above the ground. AJ and the house are both perpendicular to the ground. The angles between the top of house, the mirror, and the ground and between AJ's eyes, the mirror, and the ground are congruent as shown in the image below. What is the height of the house?

Respuesta :

MissPhiladelphia
The two triangles formed are similar triangles and this can be solved by ratio and proportion.
Let x be the height of the house.
5.5 / x = 5 / 20
Solving for x:
x = 22 ft
The height of the house is 22 feet.

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