Problem:
A angle-side-angle triangle has angle $47 {}^{\circ}$, a side of length $\frac{17}{2}$ and an angle of measure $19 {}^{\circ}$. Determine points to define lines for the triangle's altitude, cevian, median, and symmedian lines.
Answer:
Altitude: $\left(
\begin{array}{cc}
 \frac{17}{2} & 0 \\
 \frac{17}{2} \sin ^2(43 {}^{\circ}) & \frac{17}{4} \cos (4 {}^{\circ}) \\
\end{array}
\right)$ 
Median: $\left(
\begin{array}{cc}
 \frac{17}{2} & 0 \\
 \frac{17}{4} \sin (19 {}^{\circ}) \sin (43 {}^{\circ}) \sec (24 {}^{\circ}) & \frac{17}{4} \sin (19 {}^{\circ}) \cos (43 {}^{\circ}) \sec (24 {}^{\circ}) \\
\end{array}
\right)$ 
Symmedian: $\left(
\begin{array}{cc}
 \frac{17}{2} & 0 \\
 \frac{17 \sin (19 {}^{\circ}) \sin (43 {}^{\circ}) \cos (24 {}^{\circ})}{\sin (4 {}^{\circ})+\sin (42 {}^{\circ})+2} & \frac{17 \sin (19 {}^{\circ}) \cos (24 {}^{\circ}) \cos (43 {}^{\circ})}{\sin (4 {}^{\circ})+\sin (42 {}^{\circ})+2} \\
\end{array}
\right)$ 
Cevian: $\left(
\begin{array}{cc}
 \frac{17}{2} & 0 \\
 \frac{17}{4} \sin (19 {}^{\circ}) \sin (43 {}^{\circ}) \sec (24 {}^{\circ}) & \frac{17}{4} \sin (19 {}^{\circ}) \cos (43 {}^{\circ}) \sec (24 {}^{\circ}) \\
\end{array}
\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/geometry/triangles/31070.txt'}