An 85-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.

For this case we can model the problem as a rectangle triangle.
 We have the hypotenuse and the angle.
 We want to find the height.
 For this, we use the following trigonometric relationship:
 sine (x) = C.O / h
 Where,
 x: angle
 C.O: opposite leg
 h: hypotenuse
 Clearing C.O we have:
 C.O = 85 * sine (45)
 C.O = 60.1040764
 Round to the nearest tenth of a foot:
 C.O = 60 feet
 
 the top of the tree house is 60 feet high