Question

A triangle has sides A,B, and C. If the angle between sides A and B is `pi/3`, the angle between sides B and C is `pi/12`, and the length of B is 1, what is the area of the triangle?

Answer 1

`color(blue)(A_t = 0.4019` sq units

Explanation:

`hat A = (pi)/12, hat C = pi/3, hat B = pi - pi/12 - pi/3 = (7pi)/12, b = 1`

Applying Law of Sines,

`a / sin A = b / sin B`

`a = (1 * sin (pi/12))/sin ((7pi)/12)`

`a = 0.2679`

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

`A_t = (1/2) * 0.2679 * 1 * sin (pi/3)`

`color(blue)(A_t = 0.4019` sq units