Answer:
77.27 ft
Step-by-step explanation:
You want the length of rope between you and an anchor on a cliff if you are 20 ft from the cliff and the angle of elevation is 75°.
Cosine
We can model the geometry as a right triangle. The relation between the angle and the distances of interest is ...
Cos = Adjacent/Hypotenuse
cos(75°) = (20 ft)/(rope length)
Solving for rope length gives ...
rope length = (20 ft)/cos(75°) ≈ 77.27 ft
The length of the rope to the anchor is about 77.27 feet.
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