# A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 8, respectively. The angle between A and C is (pi)/4 and the angle between B and C is  (pi)/3. What is the area of the triangle?

Jun 3, 2018

Since it doesn’t satisfy the law of Sines, we can’t form a triangle with the given measurements

#### Explanation:

$a = 12 , b = 8 , \hat{A} = \frac{\pi}{3} , \hat{B} = \frac{\pi}{4}$

As per the Law of Sines,

$\frac{a}{\sin} A = \frac{b}{\sin} B = \frac{c}{\sin} C$

$\frac{a}{\sin} A = \frac{12}{\sin} \left(\frac{\pi}{3}\right) = 8 \sqrt{3}$

$\frac{b}{\sin} B = \frac{8}{\sin} \left(\frac{\pi}{4}\right) = 8 \sqrt{2}$

Since it doesn’t satisfy the law of Sines, we can’t form a triangle with the given measurements