SOLUTION: before rock climbing, Fernando, who’s 5.5 ft tall, wants to know how high he will climb. He places a mirror on the ground and walks six feet backward until he can see the top of

Question 1150136: before rock climbing, Fernando, who’s 5.5 ft tall, wants to know how high he will climb. He places a mirror on the ground and walks six feet backward until he can see the top of the cliff in the mirror.
If the mirror is 34 feet from the cliffside, determine the height of the cliff.
Name the postulate or theorem you used.
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.


Let T be the top of the cliff, R the base of the cliff, M the mirror, 
F the point where she’s standing, and E her eye. 


The angle of incidence equals the angle of reflection, so the triangles △TRM and △EFM are similar. 
It implies that if the height of the cliff is h feet, then


     = .


From the proportion,  h =  = 31.166 ft is the height of the cliff.    ANSWER


You use the statement from Physics that 

    The angle of incidence equals the angle of reflection for light rays, 



and the theorem from Geometry stating that 

    if right angled triangles have congruent acute angles, then the triangles are similar
    and their corresponding legs are proportional.

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