# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 12, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

May 17, 2018

We can not form a triangle with the given measurements

#### Explanation:

$a = 2 , b = 12 , \hat{A} = \frac{5 \pi}{24} , \hat{B} = \frac{13 \pi}{24}$

As per Law of Sines, $\frac{a}{\sin} a = \frac{b}{\sin} B$

$\frac{a}{\sin} A = \frac{2}{\sin} \left(\frac{5 \pi}{24}\right) = 3.29$

$\frac{b}{\sin} B \equiv \frac{12}{\sin} \left(\frac{13 \pi}{24}\right) = 12.1$

Since values don’t satisfy the sine law, we can not form a triangle with the given measurements