# A triangle has sides A,B, and C. If the angle between sides A and B is (3pi)/8, the angle between sides B and C is pi/6, and the length of B is 10, what is the area of the triangle?

Jun 5, 2018

$\text{Area " ~~ color(red)(23.3 " sq units}$

#### Explanation:

$\frac{3}{8} \pi + \frac{\pi}{6} = \frac{13}{24} \pi$ so the third angle is $\frac{11}{24} \pi$

using the sine rule

$\frac{10}{\sin \left(\frac{11}{24} \pi\right)} = \frac{c}{\sin \left(\frac{3}{8} \pi\right)}$

c ~~color(red)( 9.32

area=$\frac{1}{2}$absinC

area=$\frac{1}{2} \times 10 \times \textcolor{red}{9.32} \times \sin \left(\frac{\pi}{6}\right)$

#"Area = (1/2) * 10 * color(red)(9.32) * (1/2)

$\text{Area " = (10/4) * 9.32 = 2.5 * 9.32 ~~ color(red)(23.3 " sq units}$