Peter walk 30 feet away from his house in places a mirror on the ground. he backed 6 feet away from the mirror so that he can see the tip of the roof. Peters eyes are 5 feet above the ground. Peter in the house are both perpendicular to the ground. The angle between the top of the house, the mirror, and the ground between Peter's eyes, the mirror, and the ground are congruent. find the height of the house

Question

Peter walk 30 feet away from his house in places a mirror on the ground.  he backed 6 feet away from the mirror so that he can see the tip of the roof. Peters eyes are 5 feet above the ground. Peter in the house are both perpendicular to the ground.  The angle between the top of the house, the mirror, and the ground between Peter's eyes, the mirror, and the ground are congruent.  find the height of the house

mathstudent55 · Answer

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mathstudent55 · Answer

The triangles are similar, so the lengths of corresponding sides are proportional.

$\dfrac{h}{5} = \dfrac{30}{6} $

Cross multiply and solve for h.