Question

What is m∠C? Round the value to the nearest degree.

Answer 1

Answer: $m\angle C=53\°$

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:

$\alpha =arcsin(\frac{opposite}{hypotenuse})$

In this case, you can identify that:

$\alpha =m\angle C\\\\opposite=AB=36\ cm\\\\hypotenuse=AC=45\ cm$

Then, substituting values into $\alpha =arcsin(\frac{opposite}{hypotenuse})$ and evaluating, you get that the measure of the angle "C" to the nearest degree, is:

$m\angle C=arcsin(\frac{36\ cm}{45\ cm})\\\\m\angle C=53\°$