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.

Guest Feb 5, 2020

#1**+1 **

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

CPhill Feb 5, 2020