Answer: [tex]m\angle C=53\°[/tex]
Step-by-step explanation:
For this exercise you need to use the Inverse Trigonometric function arcsine, which is defined as the inverse function of the sine.
Then, to find an angle α, this is:
[tex]\alpha =arcsin(\frac{opposite}{hypotenuse})[/tex]
In this case, you can identify that:
[tex]\alpha =m\angle C\\\\opposite=AB=36\ cm\\\\hypotenuse=AC=45\ cm[/tex]
Then, substituting values into [tex]\alpha =arcsin(\frac{opposite}{hypotenuse})[/tex] and evaluating, you get that the measure of the angle "C" to the nearest degree, is:
[tex]m\angle C=arcsin(\frac{36\ cm}{45\ cm})\\\\m\angle C=53\°[/tex]
