# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 4, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Jun 10, 2018

color(gray)(" Since " a > b, " but " hat A < hat B, " such a triangle cannot exist."

#### Explanation:

$a = 5 , \hat{A} = \frac{3 \pi}{8} , b = 4 , \hat{b} = \frac{13 \pi}{24}$

color(indigo)("THEOREM. A greater angle of a triangle is opposite a greater side."

color(indigo)("Let ABC be a triangle in which angle ABC is greater than angle "

color(indigo)("BCA; then side AC is also greater than side AB"

color(gray)(" Since " a > b, " but " hat A < hat B, " such a triangle cannot exist."