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 10, what is the area of the triangle?

Answer 1

`color(brown)(A_t = (1/2) * a * b * sin C = 10.6 " sq units"`

Explanation:

`hat A = pi/12, hat C = pi/4, b = 10`

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

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]()

Applying the law of sines,

`a = (b * sin A ) / sin B = (10 * sin (pi/12)) / sin ((2pi)/3) ~~ 3 " units"`

`"Area of the triangle " A_t = (1/2) * a * b * sin C`

`color(brown)(A_t = (1/2) * 3 * 10 * sin (pi/4) = 10.6 " sq units"`