Answer:
about 626.1 ft
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle. The given angle is opposite the given side, and we are asked to find the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
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Solving for the hypotenuse, we get ...
Hypotenuse = Opposite/Sin
cable length = (balloon height)/sin(53°) = (500 ft)/0.79864
cable length ≈ 626.1 ft
