# 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  (pi)/24. What is the area of the triangle?

Apr 8, 2018

color(red)("Since the given measurements ") color(maroon)(" do not satisfy the Sine Law"), color(red)(" we cannot form a triangle."

#### Explanation:

$\hat{A} = \frac{\pi}{24} , a = 6 , \hat{B} = \frac{17 \pi}{24} , b = 7 , \text{ To find the area of } \Delta$

According to Law of Sines, $\frac{a}{\sin} A = \frac{b}{\sin} B$

$\frac{a}{\sin} A = \frac{6}{\sin} \left(\frac{\pi}{24}\right) = 8.49$

$\frac{b}{\sin} B = \frac{7}{\sin} \left(\frac{17 \pi}{24}\right) = 8.82$

Since the given measurements do not satisfy the Sine Law, we cannot form a triangle.