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You are at the NC Hot Air Balloon Festival in Statesville, NC. A 90 90 foot rope is currently securing the hot air balloon to the ground so the kids can admire it. The angle of depression from the balloon to the stake in the ground is 62∘ 62 ∘ . Find the height of the balloon from the ground. Find your answer to the nearest foot.

Answer :

sqdancefan

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.

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