I am reading Head First Physics, and on page 362 it discusses using the inverse of sin, cos, or tan to work out an angle.
I understand that without using Pythagoras I must circle the table where I can use the inverse of either sin, cos, or tan to get the angle. This is determined by what the available ratios are.
I can see that the second row (triangle B) does not have cos circled for number 0.913 as the ratio is missing and we were told not to use Pythagoras. My confusion however, is why the inverse of cos 0.913 gives 24.076 when the answer is 24.2? The rest of the table, whether circled or not, seems to give the correct answer for the angle column...
Here is a picture of the table:
It looks like either a typo or rounding error. For triangle b, if you actually use the Pythagorean Theorem, you find that the length of the hypotenuse is $\sqrt{481}$, so $\cos(\theta) = \frac{20}{\sqrt{481}} \approx 0.912$ instead of $0.913$. If you them compute $\cos^{-1}(0.912)$ you get approximately $24.2^{\circ}$.