# A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 5, respectively. The angle between A and C is (pi)/12 and the angle between B and C is  (pi)/6. What is the area of the triangle?

##### 1 Answer

the triangle does not exist

#### Explanation:

checking by the Sine Law:

$\frac{a}{\sin} A \ne \frac{b}{\sin} B$

this means

$\frac{12}{\sin} \left(\frac{\pi}{6}\right) \ne \frac{5}{\sin} \left(\frac{\pi}{12}\right)$

$24 \ne 19.3185$