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You hike 400 feet up a steep hill that has a 25 degrees angle of elevation as shown in the diagram.

Give each side and angle measure rounded to the nearest whole number.

You hike 400 feet up a steep hill that has a 25 degrees angle of elevation as shown-example-1
User MrGreg
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1 Answer

4 votes

9514 1404 393

Answer:

a = 169 ft, b = 363 ft, B = 65°

Explanation:

The mnemonic SOH CAH TOA can help you remember the necessary trig relations. For side 'a', opposite the given angle A, the appropriate relation is ...

Sin = Opposite/Hypotenuse

a = (400 ft)sin(25°) ≈ 169 ft

For side 'b', adjacent to the given angle, the appropriate relation is ...

Cos = Adjacent/Hypotenuse

b = (400 ft)cos(25°) ≈ 363 ft

Of course angle B is the complement of angle A:

B = 90° -25° = 65°

__

In summary, ...

(a, b, A) = (169 ft, 363 ft, 65°)

User MrKatSwordfish
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