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

##### 1 Answer
Mar 15, 2018

This triangle does not exist...

#### Explanation:

Just by looking at the angles, side A should correspond to the angle between side B and C, while side B should correspond to the angle between side A and C. Since side A is larger than side B but has a smaller angle corresponding to it, this triangle does not exist...

Proof with the Law of Sines:
$A = \arcsin \left(\frac{S \in B \cdot a}{b}\right)$
$A = \arcsin \left(\frac{S \in \left(\frac{5 \pi}{24}\right) \cdot 7}{5}\right) = 1.02 r a d$
pi/24 rad ≠ 1.02 rad