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The question is a follows:

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 figured 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!

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  • $\begingroup$ You mean $QR =7$ $\endgroup$ – Aqua Nov 18 '17 at 15:35
  • $\begingroup$ Yes. Thank you. $\endgroup$ – geo_freak Nov 18 '17 at 16:18
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Say angle bisector cuts $PQ$ at $S$ and let $PS=x$ then $SQ = 8-x$. By angle bisector theorem we have: $$ {x\over 8-x} = {5\over 7}$$ and you get $x$. Then use the law of cosinus for triangle $PRS$.

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  • $\begingroup$ I got the answer to be $\approx 4.410$ inches. $\endgroup$ – geo_freak Nov 18 '17 at 16:22

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