Problem:
A side-angle-side triangle has sides $\frac{23}{2}$ and $\frac{13}{2}$ and an angle $59 {}^{\circ}$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines.
Answer:
Cevian: $\left(
\begin{array}{cc}
 \sqrt{\frac{1}{2} (349-299 \sin (31 {}^{\circ}))} & 0 \\
 \frac{13 \sqrt{\frac{1}{2} (349-299 \sin (31 {}^{\circ}))} (23 \sin (31 {}^{\circ})-13)}{4 (299 \sin (31 {}^{\circ})-349)} & -\frac{299 \sqrt{\frac{1}{2} (349-299 \sin (31 {}^{\circ}))} \cos (31 {}^{\circ})}{4 (299 \sin (31 {}^{\circ})-349)} \\
\end{array}
\right)$ 
Symmedian: $\left(
\begin{array}{cc}
 \sqrt{\frac{1}{2} (349-299 \sin (31 {}^{\circ}))} & 0 \\
 -\frac{13 \sqrt{698-598 \sin (31 {}^{\circ})} (23 \sin (31 {}^{\circ})-13) (299 \sin (31 {}^{\circ})-349)}{2 (89401 \sin (28 {}^{\circ})+575575 \sin (31 {}^{\circ})-517624)} & \frac{299 \sqrt{698-598 \sin (31 {}^{\circ})} (299 \sin (31 {}^{\circ})-349) \cos (31 {}^{\circ})}{2 (89401 \sin (28 {}^{\circ})+575575 \sin (31 {}^{\circ})-517624)} \\
\end{array}
\right)$ 
Median: $\left(
\begin{array}{cc}
 \sqrt{\frac{1}{2} (349-299 \sin (31 {}^{\circ}))} & 0 \\
 \frac{169-299 \sin (31 {}^{\circ})}{4 \sqrt{698-598 \sin (31 {}^{\circ})}} & \frac{299 \cos (31 {}^{\circ})}{4 \sqrt{698-598 \sin (31 {}^{\circ})}} \\
\end{array}
\right)$ 
Altitude: $\left(
\begin{array}{cc}
 \sqrt{\frac{1}{2} (349-299 \sin (31 {}^{\circ}))} & 0 \\
 \frac{(13-23 \sin (31 {}^{\circ}))^2}{2 \sqrt{698-598 \sin (31 {}^{\circ})}} & -\frac{23 (23 \sin (31 {}^{\circ})-13) \cos (31 {}^{\circ})}{2 \sqrt{698-598 \sin (31 {}^{\circ})}} \\
\end{array}
\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/geometry/triangles/79885.txt'}