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

Answer:

the top of the tree house is 60 feet high