Question

A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 10, respectively. The angle between A and C is `(7pi)/24` and the angle between B and C is `(3pi)/8`. What is the area of the triangle?

Answer 1

Since `color(maroon)(a / sin A != b / sin B, " we cannot form a triangle with the given measurements"`

Explanation:

`a = 12, b = 10, hat A = (3pi)/8, hat B = (7pi)/24`

`color(crimson)("As per the Law of sines,"`

`color(crimson)(a / sin A = b / sin B = c / sin C`

`a / sin A = 12 / sin ((3pi)/8) = color(brown)(12.99`

`b / sin B = 10 / sin ((7pi) / 24) = color(indigo)(12.6`

Since `color(maroon)(a / sin A != b / sin B, " we cannot form a triangle with the given measurements"`