SOLUTION: Brooke wanted to measure the height of the tree in her backyard. Brooke placed the mirror on the ground 32 ft. away from the tree and then walked backwards until she was able to se
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Question 559509: Brooke wanted to measure the height of the tree in her backyard. Brooke placed the mirror on the ground 32 ft. away from the tree and then walked backwards until she was able to see the top of the tree in the mirror. Her eyes are 5 ft. above the ground and she is 8 ft. from the mirror. Using similar triangles, find the height of the tree. Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! That tree is 20 feet tall. The tree (RT, Root to Top) and Brooke (FE, Feet to Eye) are the short legs of similar right triangles MRT and MFE. (The ground, and red mirror M are perfectly level and horizontal. The green tree and blue-eyed Brooke stand perfectly straight, vertical, and perpendicular to the ground. As a consequence the angles at R and F are right angles, and therefore congruent to each other. The mirror reflects symmetrically, so the angles at M are congruent too. That makes the remaining pair of angles (at T and E) congruent, and the triangles similar).
All the sides'lengths in MRT are 4 times the length of the corresponding sides in MFE. So RT is 4 times FE, or = 20.
