Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(pi)/4`, the angle between sides B and C is `pi/6`, and the length of B is 1, what is the area of the triangle?

Answer 1

`color(indigo)(A_t = 1/2 a b sin C ~~ 0.183, " sq. units"`

Explanation:

`hat A = pi/6, hat C = pi/4, hat B = (7pi)/12, b = 1`

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

`a = (b * sin A) / sin B = (1 * sin (pi/6)) / sin ((7pi)/12)`

`a ~~ 0.5176`

`"Area of D" Delta = A_t = 1/2 a b sin C`

`color(indigo)(A_t = 1/2 * 0.5176 * 1 * sin (pi/4) ~~ 0.183, " sq. units"`