Question

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?

Answer 1

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

Explanation:

`a = 5, hat A = (3pi)/8, b = 4, hat b = (13pi) / 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."`