# A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12 and the angle between sides B and C is pi/6. If side B has a length of 7, what is the area of the triangle?

Jul 25, 2018

Angle C=$\frac{5 \pi}{12}$ given, angle A=$\frac{\pi}{6} \left[= \frac{2 \pi}{12}\right]$ also given

so angle B =$\frac{12 \pi - 7 \pi}{12} = \frac{5 \pi}{12}$

This means the triangle is isosceles and side c will be length 7.

Area is $\frac{1}{2}$absinC

Area=$\frac{1}{2} \times 7 \times 7 \times \sin \left[\frac{\pi}{6}\right]$

Area =$\frac{1}{2} \times 49 \times \frac{1}{2}$

Area=$\frac{49}{4}$

Area =$12 \frac{1}{4} u n i t {s}^{2}$