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Question

anonymous · Answer

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. 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:



Part 1: Prove the triangles are similar.
Part 2: Determine the height of the house.

anonymous · Answer

attachment

anonymous · Answer

@Zale101

zale101 · Answer

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Both triangles have 90, so by AA (Angle Angle) the two triangles have similar postulates because the two angles of the triangle are congruent to two angles of another triangle. That indicates that the two triangles are similar to each other.

zale101 · Answer

To learn more about the AA postulate go to: http://www.mathwarehouse.com/geometry/similar/triangles/similar-triangle-theorems.php

zale101 · Answer

Part 2: Determine the height of the house.
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Paul walked 25 feet away from the house, so the base of the triangle is 25 feet
paul placed a mirror and walked 5 feet away from it, so the base f te smaller triangle is 5 feet

When Paul's eyes are 6 feet above the ground, so that's his height and the hypotenuse of his triangle (small triangle) is 6 feet