# 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 27, what is the area of the triangle?

Area $= 182.25 \text{ " }$square units

#### Explanation:

We will take the side $b = 27$ as the base of the triangle
Angle $A = \frac{\pi}{12}$ and angle $C = \frac{5 \pi}{6}$

We need the height $h$ to solve for the Area$= \frac{1}{2} b h$

Solve h

$b = h \cdot \cot A + h \cot C$

$h = \frac{b}{\cot A + \cot C}$

h=27/(cot (pi/12)+cot ((5pi)/6)

$h = 13.5$

Solve Area:

Area$= \frac{1}{2} b h$

Area=1/2(27)(13.5

Area$= 182.25 \text{ }$square units

have a nice day!