Answer:
1) Mistakes:
The adjacent side that is next to the missing angle is not 16, so [tex]x=cos^{-1}(\frac{16}{20})[/tex] is incorrect.
He should have used [tex]x=sin^{-1}(\frac{opposite}{hypotenuse})[/tex] to find the missing angle.
2) The correct solution is:
[tex]x[/tex]≈53°
Step-by-step explanation:
Remember that:
1) [tex]cosx=\frac{adjacent}{hypotenuse}[/tex]
If [tex]cosx=A[/tex], then the angle whose cosine is A, can be calculated with the inverse function of the cosine:
[tex]x=cos^{-1}(A)[/tex]
2) [tex]sinx=\frac{opposite}{hypotenuse}[/tex]
If [tex]sinx=B[/tex], then the angle whose sine is B, can be calculated with the inverse function of the sine:
[tex]x=sin^{-1}(B)[/tex]
The mistakes that Bob made, are:
The adjacent side of the right triangle is not 16, so [tex]x=cos^{-1}(\frac{16}{20})[/tex] is incorrect.
Knowing that the missing angle is "x", the opposite side and the hypotenuse are the known sides. Therefore, he should have used [tex]x=sin^{-1}(\frac{opposite}{hypotenuse})[/tex] to find the missing angle.
Therefore, the correct solution is:
[tex]x=sin^{-1}(\frac{16}{20})[/tex]
[tex]x=53.13\°[/tex]≈53°
