Answer: [tex]m\angle B=46\°[/tex]
Step-by-step explanation:
For this exercise you need to use the Inverse Trigonometric function arccosine, which is defined as the inverse function of the cosine.
Then, to find an angle α, this is:
[tex]\alpha =arccos(\frac{adjacent}{hypotenuse})[/tex]
In this case, you can identify that:
[tex]\alpha =m\angle B\\\\adjacent=AB=20\ cm\\\\hypotenuse=BC=29\ cm[/tex]
Then, substituting values into [tex]\alpha =arccos(\frac{adjacent}{hypotenuse})[/tex] and evaluating, you get that the measure of the angle "B" to the nearest degree, is:
[tex]m\angle B=arccos(\frac{20\ cm}{29\ cm})\\\\m\angle B=46\°[/tex]
