# 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/12. If side B has a length of 48, what is the area of the triangle?

Jan 28, 2016

4299.322531

#### Explanation:

lets draw a perpendicular line on B .
suppose, the length of the perpendicular is D
now, the problem says, the angle between A and B is $\frac{5 \pi}{12}$
now,
in, $\triangle A B D$,
$\frac{D}{B} = \tan \left(\frac{5 \pi}{12}\right)$
$\mathmr{and} , D = B \tan \left(\frac{5 \pi}{12}\right)$
now, by putting the values, B=48 and tan$\frac{5 \pi}{12}$ ,
$D = 48 \cdot 3.732050808$
$\mathmr{and} , D = 179.1384388$
so,
The area of $\triangle A B C = \frac{1}{2} \cdot B \cdot D$
now, by putting the value of B and D in the above equation, we get,
$\triangle A B C = \frac{1}{2} \cdot 48 \cdot 179.1384388 = 4299.322531$