A hill frequently used for sled riding has an angle of elevation of 25 degrees at it's bottom. If the length of a sledders ride is 52 ft, estimate the height of the hill.

Question

Mathematics

Cristian Moreno

21 September, 04:14

A hill frequently used for sled riding has an angle of elevation of 25 degrees at it's bottom. If the length of a sledders ride is 52 ft, estimate the height of the hill.

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Answers (1)

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Octavio Hurst · Answer 1

22 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the necessary relationship. If the sledding slope is modeled as the hypotenuse of a right triangle with 25° as one of the acute angles, the side opposite the angle (the hill height) satisfies ...

Sin = Opposite/Hypotenuse

Opposite = Hypotenuse * Sin

height = (52 ft) sin (25°) ≈ 22.0 ft

The height of the hill is about 22 feet.