The two sides of the triangle are 3√3 cm and 2 cm, and the angle between them is 60 °. Find a third party.

Knowing the two sides of the triangle and the angle between them, the third side can be found by the cosine theorem. The square of any side of a triangle is equal to the sum of the squares of the other two sides without twice the product of these sides by the cosine of the angle between them.

a ^ 2 = b ^ 2 + c ^ 2 – 2bc * cos 60 °

We have b = 3√3 cm, c = 2 cm.

a ^ 2 = (3√3) ^ 2 + 2 ^ 2 – 2 * 3√3 * 2 * cos 60o;

a ^ 2 = 9 * 3 + 4 – 12√3 * 1/2 = 27 + 4 – 6√3 = 31 – 6√3;

a = √ (31 – 6√3).

Answer. √ (31 – 6√3) cm.