Problem:
A side-angle-side triangle has sides $\frac{25}{2}$ and $2$ and an angle $50 {}^{\circ}$. Determine the area, circumradius, inradius, and semiperimeter of the triangle.
Answer:
Inradius: $\frac{5}{\sqrt{\frac{2 \left(\sqrt{641-200 \sin (40 {}^{\circ})}+29\right) (200 \sin (40 {}^{\circ})-641)}{-100 \sin (10 {}^{\circ}) \left(\sqrt{641-200 \sin (40 {}^{\circ})}-29\right)+58 \sqrt{-20000 \sin (10 {}^{\circ})-256400 \sin (40 {}^{\circ})+430881}+741 \sqrt{641-200 \sin (40 {}^{\circ})}+35989 \sin (40 {}^{\circ})-841 \sqrt{641-200 \sin (40 {}^{\circ})} \sin (40 {}^{\circ})-58667}}}$ 
Semiperimeter: $\frac{1}{4} \left(\sqrt{641-200 \sin (40 {}^{\circ})}+29\right)$ 
Circumradius: $\frac{1}{4} \sqrt{641-200 \sin (40 {}^{\circ})} \sec (40 {}^{\circ})$ 
Area: $\frac{25}{2} \cos (40 {}^{\circ})$
{'source': 'AMPS', 'file': 'amps/mathematica/geometry/triangles/75688.txt'}