An Interesting Triangle Property

I'm considering this one for my "Almost Pythagorean" file. I came across this recently and found it interesting. The Pythagorean Theorem is actually a property about triangles with 90 degree angles; but this one is a property of all triangles that contain a 60 degree angle at vertex A.

The "Then" implied by the above is that

The derivation is not too difficult and might well be presented to a good pre-calc student as a challenge. If you don't want me to spoil it, stop reading now until you have tried it.... It makes me wonder what we could come up with if we started with a thirty-degree angle.

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