Question

A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is `(pi)/12` and the angle between B and C is `(5pi)/6`. What is the area of the triangle?

Answer 1

`color(red)(A_t = (1/2) a b sin C = (1/2) * 5 * 8 * sin (pi/12) = 5.18 " sq units"`

Explanation:

`a = 5, b = 8, hat A = (5pi)/6, hat B = pi/12`

To find the area of the triangle.

`hat C = pi - (5pi)/6 - pi/12 = pi/12`

It's an isosceles triangle with `hat B = hat C " & hence " b = c = 8`

Formula for Area of triangle, knowing 2 sides and included angle

`color(red)(A_t = (1/2) a b sin C = (1/2) * 5 * 8 * sin (pi/12) = 5.18 " sq units"`