Given: triangle PQR, area of triangle PQR=50, m

14.501

Step-by-step explanation:

Another tricky question! Took me about half an hour...

Construct OQConsider triangle PQO, it is constructed by two radii, thus this triangle is isosceles, m∠PQO must also have 36°, then m∠POQ is 108°. Consider triangle QOR, it is also constructed by two radii, thus this triangle is also isosceles, m∠OQR must be 54°, then m∠QOR is 72°. Find PQ and QR in terms of r (radius) with the law of cosines. Set up an equation for the area of the triangle. With the help from a calculator, we get two solutions: Since lengths cannot be negative, the positive solution is our only solution. Multiply it by 2 to get PR.

Now let me receive treatment for my headache...