Question

If sides A and B of a triangle have lengths of 18 and 12 respectively, and the angle between them is `(2pi)/3`, then what is the area of the triangle?

Answer 1

Area of triangle `color(chocolate)(A_t = 93.53` sq. units

Explanation:

Formula for area of triangle `A_t = (1/2) a b sin C`

Given `a = 18, b = 12, hat C = (2pi)/3`

`A_t = (1/2) * 18 * 12 * sin ((2pi)/3)`

`A_t =( 9 * 12 * sqrt3) / 2 = 54 sqrt3 = 93.53`