Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6` and the angle between sides B and C is `pi/12`. If side B has a length of 3, what is the area of the triangle?

Answer 1

Area `color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25` sq units

Explanation:

Law of Sines `a / sin A = b / sin B = c / sin C`

Area of triangle `A_t =.(1/2) a b sin C`

`b = 3, hat A = pi/12, hat C = (5pi)/6, hat B = pi - pi / 12 - (5pi)/6 = pi/12`

It’s an isosceles triangle with angles #hat A = hat B = pi/12%

`:. b = a = 3`

Area `color(maroon)(A_t = (1/2) * 3 * 3 * sin ((5pi)/6) = 2.25` sq units