Question

A triangle has sides A, B, and C. The angle between sides A and B is `(3pi)/4` and the angle between sides B and C is `pi/12`. If side B has a length of 12, what is the area of the triangle?

Answer 1

`color(maroon)("Area of " Delta = 26.35 " sq units"`

Explanation:

`hat A = pi/12, hat C = (3pi)/4, hat B = pi/6, b = 12`

To find Area of the triangle.

Applying the Law of Sines,

`a = (b * sin A) / sin B = (12 * sin (pi/12)) / sin (pi/6) = 6.21`

`"Area of " Delta = (1/2) a b sin C = (1/2) * 12 * 6.21 * sin ((3pi)/4)`

`color(maroon)("Area of " Delta = 26.35 " sq units"`