Answer:
79 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relationship between the side opposite an angle and the hypotenuse is ...
Sin = Opposite/Hypotenuse
In the right triangle of interest, the height of the balloon is opposite the angle of depression, and the length of the rope is the hypotenuse. Then the ballon height is given by ...
sin(62°) = height/(90 ft)
Multiplying by 90 ft, we find ...
height = (90 ft)sin(62°) ≈ 79.465 ft
The height of the balloon is about 79 feet.
