Question

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?

Answer 1

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((SinB*a)/b)`
`A= arcsin((Sin((5pi)/24)*7)/5)= 1.02 rad`
`pi/24 rad ≠ 1.02 rad`