A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6 and the angle between sides B and C is pi/12. If side B has a length of 3, what is the area of the triangle?

Jun 3, 2018

Area color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25 sq units

Explanation:

Law of Sines $\frac{a}{\sin} A = \frac{b}{\sin} B = \frac{c}{\sin} C$

Area of triangle ${A}_{t} = . \left(\frac{1}{2}\right) a b \sin C$

$b = 3 , \hat{A} = \frac{\pi}{12} , \hat{C} = \frac{5 \pi}{6} , \hat{B} = \pi - \frac{\pi}{12} - \frac{5 \pi}{6} = \frac{\pi}{12}$

It’s an isosceles triangle with angles hat A = hat B = pi/12%

$\therefore b = a = 3$

Area color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25# sq units