Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/4` and the angle between sides B and C is `pi/12`. If side B has a length of 9, what is the area of the triangle?

Answer 1

`color(green)("Area of Triangle " color(maroon)(A_t = 8.56 color(green)(" sq units")`

Explanation:

`hat A = pi/12, hat C = pi/4, b = 9`

`hat B = pi - pi/12 - pi/4 = (2pi)/3`

Applying the law of sines,

a = (b * sin A) / sin B = (9 * sin (pi/12)) / sin ((2pi)/3) = 2.69#

Area of triangle, known two sides and the included angle is

`A_t = (1/2) a b sin C = (1/2) * 2.69 * 9 * sin (pi/4) = 8.56`