The sides of the triangle are 5 cm and 3 cm, and the angle between them is 60. Find the third side of the triangle.

To calculate the third side of a triangle, we use the cosine theorem, according to which the square of one of the sides of a triangle is equal to the sum of its other two sides in a square minus the double product of these sides by the cosine of the angle between them:

a ^ 2 = b ^ 2 + c ^ 2 – 2bccos α.

Let’s assume that AB = 5 cm, BC = 3 cm, and the angle ∠B = 60 °.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * cos 60 °;

cos 60 ° = ½;

AC ^ 2 = 5 ^ 2 + 3 ^ 2 – 2 * · 5 · * 3 · * ½ = 25 + 9 – 15 = 19;

AC = √19 = 4.36 cm.

Answer: The length of the third side of the AC triangle is 4.36 cm.