Question

A triangle has sides A,B, and C. If the angle between sides A and B is `(pi)/3`, the angle between sides B and C is `pi/4`, and the length of B is 5, what is the area of the triangle?

Answer 1

Area `A_t color(brown)(= 7.92` sq units

Explanation:

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

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

`hat A = pi/4, hat C = pi/3, hat B = (5pi)/12, b = 5`

`a = (5 * sin (pi/4)) / sin ((5pi)/12) = 3.66`

`A_t= (1/2) * 3.66 * 5 * sin (pi/3) color(brown)(= 7.92` sq units