# A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 9, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (7pi)/24. What is the area of the triangle?

Jun 10, 2018

color(red)("Triangle cannot exist with the given measurements."

#### Explanation:

color(purple)(a = 6, hat A = (7pi)/24, b = 9, hat B = (5pi) / 24

To find the area of the triangle.

THEOREM . $\text{A greater angle of a triangle is opposite a greater side. Let ABC be a triangle in which angle ABC is greater than angle BCA; then side AC is also greater than side AB}$

color(brown)("Though " hat A" is greater than "hat B, " side a is less than b."

Hence a triangle cannot exist with the given measurements.