Question

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?

Answer 1

`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 . `"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.