The two sides of the triangle are 6 and 10 cm, and the angle between them is 120 degrees.

The two sides of the triangle are 6 and 10 cm, and the angle between them is 120 degrees. a) Find the perimeter of the triangle b) Find the area of the triangle.

The unknown side of a triangle is determined by the cosine theorem, according to which the square of the side of a triangle is equal to the sum of the squares of the other two sides minus their double product by the cosine of the angle between them:

c ^ 2 = a ^ 2 + b ^ 2 – 2 * a * b * cos α = 6 ^ 2 + 10 ^ 2 – 2 * 6 * 10 * cos 120 ° = 36 + 100 + 60 = 196 = 142;

c = 14 cm.

The perimeter of a triangle is equal to the sum of the lengths of its sides:

P = 6 + 10 + 14 = 30 cm.

The area of a triangle is equal to half the product of its two sides by the sine of the angle between them:

S = 0.5 * a * b * sin α = 0.5 * 6 * 10 * sin 120 ° = 0.5 * 6 * 10 * √3 / 2 = 15√3 ≈ 25.98 cm2.