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 22, what is the area of the triangle?

Answer 1

Area of the `Delta ABC` `color(indigo)(A_t = 88.5781` sq units

Explanation:

Third angle `hat B = pi - hat A - hat C = pi - pi / 12 - (3pi) / 4 = pi / 6`

`22 / sin (pi / 6 )= a / sin (pi / 12) = c / sin ((3pi) /4)`

`c = (22 * sin ((3pi)/4)) / sin (pi/ 6) = (22 * (1/sqrt2)) / (1/2) = 22 sqrt 2`

Using SAS formula to calculate the area of the triangle,

`A_t = (1/2) b c sin A = (1/2) * 22 * 22 sqrt 2 * sin (pi / 12)`

`color(indigo)(A_t = 88.5781` sq units