Find the side AC of the triangle ABC if AB = 5√2cm, Bc = 4cm, angle B = 135 °.

According to the cosine theorem, the square of the side of a triangle can be found as the sum of the squares of the other two sides minus their double product by the cosine of the angle opposite the desired side. Means:
AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * cos B = (5√2) ^ 2 + 4 ^ 2 – 2 * 5√2 * 4 * cos 135 °;
AC ^ 2 = 50 + 16 – 2 * 5√2 * 4 * (- √2 / 2) = 66 + 40 = 106;
AC = √106 ≈ 10.3 cm.