|NOT A REAL PLANE ON FIRE. Source.|
Note: Figure not drawn to scale.
In the figure above, P is the center of a circle, and Q and R lie on the circle. If the area of the sector PQR is 25π3 and the length of arc QR is 5π2, what is the measure of ∠RPQ?
Put your answers in the comments. I'll post the solution Monday. Good luck!
UPDATE: props and ring kisses to Elias, who answered on Facebook, and to JD, who did his thing right here on the site (and spelled out the solution quite elegantly). Side note: I'd love to be able to integrate those two commenting systems -- is that possible?
Solution below the cut: