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An 80-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot.

 Feb 5, 2020
 #1
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The rope  will be the hypotenuse of a 45-45-90 right triangle

 

So....the height of the  treehouse  = H =    the  distance form where the rope touches the ground to the tree

 

So  ....using the Pythagorean Theorem  we have that

 

H^2 + H^2   = 80^2

 

2H^2  = 6400      divide both sides by 2

 

H^2  = 3200      take the positive square root

 

H  =sqrt (3200)  = sqrt (2 * 1600)   =  40 sqrt (2) ≈  56.6  ft = height of treehouse 

 

 

 

cool cool cool

 Feb 5, 2020

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