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.

a.) 48m

b.) 158m

m<B.) 73 degrees

Step-by-step explanation:

9514 1404 393

  a = 169 ft, b = 363 ft, B = 65°

Step-by-step 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°)