A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 7, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (7pi)/24. What is the area of the triangle?

The triangle does not exist

Explanation:

From the given data:

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 7, respectively. The angle between A and C is 13π/24 and the angle between B and C is 7π/24. What is the area of the triangle?

sides $a = 2$ and $b = 7$ and angle $B = \frac{13 \pi}{24}$ and angle $A = \frac{7 \pi}{24}$

By the Sine Law

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

But

$\frac{2}{\sin} \left(\frac{7 \pi}{24}\right)$ not equal to $\frac{7}{\sin} \left(\frac{13 \pi}{24}\right)$

The triangle does not exist.

God bless...I hope the explanation is useful.