The two sides of the triangle are 6 cm and 4 cm, and the angle between them is 120 °

The two sides of the triangle are 6 cm and 4 cm, and the angle between them is 120 ° Find the third side of the area of the triangle.

1) What is the third side of the triangle?

Using the cosine theorem, we find the third side of the triangle, we have:

c ^ 2 = 6 ^ 2 + 4 ^ 2 – 2 * 6 * 4 * cos120˚ = 6 ^ 2 + 4 ^ 2 – 2 * 6 * 4 * cos (180˚ – 60˚) = 6 ^ 2 + 4 ^ 2 + 2 * 6 * 4 * cos60˚ = 36 + 16 + 48 * (1/2) = 52 + 24 = 76.

c = √76 = 2√19 (cm) or c = -√76 = -2√19 – does not satisfy the condition of the problem.

What is the area of a triangle?

S = (6 * 4 * sin120˚) / 2 = (24 * sin120˚) / 2 = 12 * (√3 / 2) = 6√3 (cm2).

Answer: the third side of the triangle is 2√19 cm, the area of the triangle is 6√3 cm2.