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) 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°