A triangle has sides A, B, and C. Sides A and B have lengths of 9 and 4, respectively. The angle between A and C is (pi)/12 and the angle between B and C is  (2pi)/3. What is the area of the triangle?

Oct 2, 2016

Let angle beween A and C $= \beta = \frac{\pi}{12}$

Angle beween B and C $= \alpha = \frac{2 \pi}{3}$

So angle beween A and B $= \gamma = \pi - \frac{\pi}{12} - \frac{2 \pi}{12} = \frac{\pi}{4}$

Again sides $A = 9 \mathmr{and} B = 4$

The area of the triangle

$\Delta = \frac{1}{2} \times A \times B \times \sin \gamma$

$\implies \Delta = \frac{1}{2} \times 9 \times 4 \times \sin \left(\frac{\pi}{4}\right)$

$= 18 \times \frac{1}{\sqrt{2}} = 9 \sqrt{2} s q u n i t$