A triangle has sides A, B, and C. Sides A and B have lengths of 9 and 7, respectively. The angle between A and C is (3pi)/8 and the angle between B and C is  (pi)/3. What is the area of the triangle?

Jun 18, 2018

50

Explanation:

S(area of the triangle)
$= A \cdot {h}_{A}$(height relative to A)
$= A \cdot B \cdot \sin$(angle between A and B)
$= A \cdot B \cdot \sin \left(\pi - \frac{3}{8} \pi - \frac{1}{3} \pi\right)$
$= A \cdot B \cdot \sin \left(\frac{7}{24} \pi\right)$
$\approx 9 \cdot 7 \cdot 0.79$
$\approx 50$