Question

The angle bisectors of AABC are AV, B, and CV. They meet at a single point V.

(In other words, V is the incenter of AABC.)
Suppose SV = 12, CV= 15, m L SBT=92°, and m ZUAV= 24°
Find the following measures.
Note that the figure is not drawn to scale.

Answer 1

1. m ZUAV = 24°
2. m L SBT = 92°
3. m L SAV = m L SBT / 2 = 92° / 2 = 46°
4. m L CAV = 180° - m L SAV - m ZUAV = 180° - 46° - 24° = 110°
5. m L SCV = m L CAV = 110°
6. m L SVB = 180° - m L SAV - m L SCV = 180° - 46° - 110° = 24°
7. m L CVB = 180° - m L CAV - m L SVB = 180° - 110° - 24° = 46°
8. m L SVT = 180° - m L SBT = 180° - 92° = 88°
9. To find the area of the triangle

Area = (1/2) x (12)(15)sin(92)