Question

A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 7, respectively. The angle between A and C is `(17pi)/24` and the angle between B and C is `(5pi)/24`. What is the area of the triangle?

Answer 1

`" Since "color(brown)(a / sin A != b / sin B) , color(indigo)(" we can not form a triangle with the given measurements."`

Explanation:

`hat A = (5pi)/24, a = 6, hat B = (17pi)/24, b = 7`

As per the Law of Sines,

`a / sin A = b / sin B`

`a / sin A = 6 / sin ((5pi)/24) = 9.86`

`b / sin B = 7 / sin ((7pi)/24) = 8.82`

`" Since "color(brown)(a / sin A != b / sin B) , color(indigo)(" we can not form a triangle with the given measurements."`