Question

A 100-foot rope from the top of a tree house to the ground forms a 45 degree 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

Answer 1

The top of the tree house is 70.71ft high

Explanation:

Kindly find attached rough sketch of the problem for your reference.

From the sketch we see that the rope at 45° and the tree house form a right angle triangle

Applying

SOH CAH TOA formula

using SOH

sin θ= h/100

h= sinθ*100

h= sin(45)*100

h= 0.7071*100

h= 70.71ft