Answer: first option.
Step-by-step explanation:
Given the right triangle shown in the figure, to calculate the measure of the angle m∠C, you can use the inverse function of the cosine:
[tex]\alpha=arccos(\frac{adjacent}{hypotenuse})[/tex]
You can identify in the figure, that, for the angle ∠C:
[tex]\alpha=\angle C\\adjacent=7\\hypotenuse=15[/tex]
Then, since you know the lenght of the adjacent side and the lenght of the hypotenuse, you can substitute these values into [tex]\alpha=arccos(\frac{adjacent}{hypotenuse})[/tex].
Therefore, the measure of the angle ∠C is:
[tex]\angle C=arccos(\frac{7}{15})\\\\\angle C=62.2\°[/tex]
