Question

PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!

Answer 1

Answer: $m\angle R=77.2\°$

Step-by-step explanation:

For this exercise you need to use an Inverse Trigonometric Function called "Arctangent".

By definition:

$\alpha =arctan(\frac{opposite}{adjacent})$

You must observe carefully the triangle PQR shown in the picture attached.

In this case you can identify that:

$\alpha=m\angle R\\\\opposite=PQ=8\\\\adjacent=QR=3$

Therefore, knowing those values you can substitute them into  $\alpha =arctan(\frac{opposite}{adjacent})$ , as following:

 $m\angle R=arctan(\frac{PQ}{QR})\\\\m\angle R=arctan(\frac{8}{3})$

Finally, evaluating, you get that the measure of the angle R is the following:

$m\angle R=77.15\°$

Rounding to the nearest tenth:

$m\angle R\approx77.2\°$