In triangle ABC cos A = 0.4, AB = 4, AC = 7. Find the square of the side BC.

This is a typical problem using the cosine theorem, when two sides AB and AC are known, and the angle between them, <A, cos A.

Cosine theorem: BC ^ 2 = AB ^ 2 + AC ^ 2 – 2 * AB * A C * cos A.

Now we define (BC ^ 2), substituting all the data:

BC ^ 2 = 4 ^ 2 + 7 ^ 2 – 2 * 4 * 7 * 0.4 = 16 + 49 – 56 * 0.4 = 65 – 22.4 = 42.6.

Where can you find BC as the root of 42.6 = 6.53.