# A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 7, respectively. The angle between A and C is (17pi)/24 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

Apr 7, 2018

$\text{ Since "color(brown)(a / sin A != b / sin B) , color(indigo)(" we can not form a triangle with the given measurements.}$

#### Explanation:

$\hat{A} = \frac{5 \pi}{24} , a = 6 , \hat{B} = \frac{17 \pi}{24} , b = 7$

As per the Law of Sines,

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

$\frac{a}{\sin} A = \frac{6}{\sin} \left(\frac{5 \pi}{24}\right) = 9.86$

$\frac{b}{\sin} B = \frac{7}{\sin} \left(\frac{7 \pi}{24}\right) = 8.82$

$\text{ Since "color(brown)(a / sin A != b / sin B) , color(indigo)(" we can not form a triangle with the given measurements.}$