Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/6` and the angle between sides B and C is `pi/12`. If side B has a length of 25, what is the area of the triangle?

Answer 1

`color(maroon)("Area of Triangle " A_t = 57.2 " sq units"`

Explanation:

`color(blue)("Given " hat A = pi/12, hat C = pi/6, hat B = pi - pi/12 - pi/6 = (3pi)/4, b = 25`

`"As per " color(red)("Law of Sines", color(green)(a / sin A = b / sin B = c / sin C`

`a / sin (pi/12) = 25 / sin ((3pi)/4) = c / sin (pi/6)`

`c = (25 * sin (pi/6)) / sin ((3pi)/4) = 17.68`

`"Area of " Delta = A_t = (1/2) *b * sin A`

`A_t = (1/2) * 25 * 17.68 * sin (pi/12) = 57.2 " sq units"`