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:

Answer 1

1) Mistakes:

The adjacent side that is next to the missing angle is not 16, so
`x=cos^(-1)((16)/(20))` is incorrect.

He should have used
`x=sin^(-1)((opposite)/(hypotenuse))` to find the missing angle.

2) The correct solution is:

`x`≈53°

Explanation:

Remember that:

1)
`cosx=(adjacent)/(hypotenuse)`

If
`cosx=A`, then the angle whose cosine is A, can be calculated with the inverse function of the cosine:

`x=cos^(-1)(A)`

2)
`sinx=(opposite)/(hypotenuse)`

If
`sinx=B`, then the angle whose sine is B, can be calculated with the inverse function of the sine:

`x=sin^(-1)(B)`

The mistakes that Bob made, are:

The adjacent side of the right triangle is not 16, so
`x=cos^(-1)((16)/(20))` is incorrect.

Knowing that the missing angle is "x", the opposite side and the hypotenuse are the known sides. Therefore, he should have used
`x=sin^(-1)((opposite)/(hypotenuse))` to find the missing angle.

Therefore, the correct solution is:

`x=sin^(-1)((16)/(20))`

`x=53.13\°`≈53°