Question

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.

Answer 1

sin 45=x/85

85 sin 45=x

x=60.104

nearest 10th is 60.1 ft

Answer 2

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
Answer:
the top of the tree house is 60 feet high