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# A 90-foot rope from the top of a tree house to the ground forms a 45∘45∘ angle of elevation from the ground. How high is the top of

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A 90-foot rope from the top of a tree house to the ground forms a 45∘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.

May 4, 2020

#1
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i'm not quite sure i'm interpreting the problem right, but i'm going to solve the problem assuming that the problem is asking you to find the leg length of a 45-45-90 triangle, where one leg is on the ground and another leg is the height of the treehouse, with the 90-foot rope being the hypotenuse.

we know that the hypotenuse of a 45-45-90 triangle with leg length $$x$$ is $$x\sqrt2$$, so we know that the leg length of a 45-45-90 triangle with hypotenuse $$y$$ is $$\frac{y}{\sqrt2} = \frac{y\sqrt2}{2}$$, so plugging in $$y = 90$$ (since the rope is the hypotenuse), we get

$$\frac{y\sqrt2}{2} = \frac{90\sqrt2}{2} = \boxed{45\sqrt2}.$$

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May 5, 2020
#2
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Great solution!!!

LuckyDucky  May 5, 2020