Question

A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is `(pi)/12` and the angle between B and C is `(5pi)/6`. What is the area of the triangle?

Answer 1

`color(crimson)("Since b > a but "hat B < hat A, " triangle cannot exist with the given measurements"`

Explanation:

`hat A = (5pi)/6, hat B = pi/12, a = 5, b = 7`

`color(purple)("THEOREM : If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side."`

`color(crimson)("Since b > a but "hat B < hat A, " triangle cannot exist with the given measurements"`