Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(2pi)/3`, the angle between sides B and C is `pi/12`, and the length of B is 12, what is the area of the triangle?

Answer 1

`:.color(brown)(A_t = (1/2) * 4.39 * 12 * sin ((2pi)/3) = 22.81 " sq units"`

Explanation:

`hat A = pi/12, hat C = (2pi)/3, hat B = pi - pi/12 - (2pi)/3 = pi/4, b = 12`

As per the Law of Sines,

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

`:. a = (b * sin A) / sin B = (12 * sin (pi/12)) / sin (pi/4) = 4.39`

`color(indigo)("Area of " Delta " " A_t = (1/2) * a * b * sin C`

`:.color(brown)(A_t = (1/2) * 4.39 * 12 * sin ((2pi)/3) = 22.81 " sq units"`