# The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. Find the length of the angle bisector of angle R.

The lengths of segments $PQ$ and $PR$ are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. Find the length of the angle bisector of angle R.

Through the Law of Sines I was able to find that the angle measure of R is approximately ${81.787}^{\circ }$ and from the Law of Cosines I figublack out that the measure of side $QR$ is 7 inches.
I am unsure of what steps I should take to find the measure of the angle bisector. Any help will be greatly appreciated!
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

RamPatWeese2w
Say angle bisector cuts $PQ$ at $S$ and let $PS=x$ then $SQ=8-x$. By angle bisector theorem we have:
$\frac{x}{8-x}=\frac{5}{7}$
and you get $x$. Then use the law of cosinus for triangle $PRS$