# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is (pi)/12 and the angle between B and C is  (5pi)/6. What is the area of the triangle?

color(crimson)("Since b > a but "hat B < hat A, " triangle cannot exist with the given measurements"
$\hat{A} = \frac{5 \pi}{6} , \hat{B} = \frac{\pi}{12} , a = 5 , b = 7$
color(purple)("THEOREM : If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side."
color(crimson)("Since b > a but "hat B < hat A, " triangle cannot exist with the given measurements"