A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/8, the angle between sides B and C is (pi)/3, and the length of B is 2, what is the area of the triangle?

May 10, 2016

Area= 0.6685

Explanation:

The triangle ABC and its given components would be as shown in the figure. Angle B= $\pi - \frac{\pi}{3} - \frac{\pi}{8} = \frac{13 \pi}{24}$. apply sine law to find side a or side c. Let us get a

a = $2 \sin \frac{\frac{\pi}{3}}{\sin} \left(\frac{13 \pi}{24}\right)$

To find the area length of perpendicular fro B upon side b is required . It would be a $\sin \left(\frac{\pi}{8}\right)$

Area= $\left(\frac{1}{2}\right) \left(2\right)$ a $\sin \left(\frac{\pi}{8}\right)$

= a $\sin \left(\frac{\pi}{8}\right)$ = $2 \sin \frac{\frac{\pi}{3}}{\sin} \left(13 \frac{\pi}{24}\right) \sin \left(\frac{\pi}{8}\right)$

=0.6685