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.

The given triangle is a right-angled triangle. This means that special trig identities can be applies

These identities are as follows:

sin (theta) = opposite / hypotenuse

cos (theta) = adjacent / hypotenuse

tan (theta) = opposite / adjacent

Now, for the unknown theta in the triangle:

The opposite side is 16 and the hypotenuse is 20

This means that we will use the sin not the cos as Bob did

The solution will be as follows:

sin (theta) = opposite / hypotenuse

sin (theta) = 16 / 20

theta = sin^-1(16/20)

theta = 53.13°

Hope this helps :)