# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 2, respectively. The angle between A and C is (17pi)/24 and the angle between B and C is  (7pi)24. What is the area of the triangle?

Jan 25, 2016

The values given do not represent any possible triangle.

#### Explanation:

Since the interior angles of a triangle must add up to $\pi$.

Interpretation 1: the angle between B and C really was meant to be $\left(7 \pi\right) 24$ as written.
If this angle is $\left(7 \pi\right) \times 24$ then it represents $84$ complete rotations i.e. the angle is 0.

Interpretation 2: the angle between B and C was meant to be $\frac{7 \pi}{24}$
The two given angles add to $\frac{17 \pi}{24} + \frac{7 \pi}{24} = \frac{24 \pi}{24} = \pi$
which implies the third angle must be $0$.

All angles of a true triangle must have measures $> 0$.