Question

Bob tried to answer the following question by finding the missing angle and rounding the answer to the nearest degree.

Here is his solution:
cos⁡x=16/20
x=cos^(-1)⁡(16/20)=36.8698976≈37°

Bob made a mistake in his work. Explain the mistake AND write the correct solution.

Answer 1

The missing angle is
`53\°`

Explanation:

Let

x-----> the missing angle

we know that

In the right triangle of the figure

The function sine of angle x is equal to divide the opposite side angle x by the hypotenuse

`sin(x)=(16)/(20)`

`x=arcsin((16)/(20))=53.13\°=53\°`

Bob's mistake was to have considered the cosine instead of the sine