Question

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

Find m∠R.

Write your answer as an integer or as a decimal rounded to the nearest tenth.


m∠R = °

Answer 1

Answer:
`m\angle R=77.2\°`

Explanation:

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

By definition:

`\alpha =arctan((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((opposite)/(adjacent))` , as following:

`m\angle R=arctan((PQ)/(QR))\\\\m\angle R=arctan((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\°`