In triangle ABC, side AB = 3 cm, side AC = 4 cm, angle A is 60 degrees. find the side of the BC

In triangle ABC, side AB = 3 cm, side AC = 4 cm, angle A is 60 degrees. find the side of the BC and the area of the trumpet ABC

Let’s find the BC side in the ABC triangle:

By the cosine theorem, we have

BC ^ 2 = AB ^ 2 + AC ^ 2 – 2 * AB * AC * cosA = 32 + 42 – 2 * 3 * 4 * cos60 = 9 + 16 – 24 * (1/2) = 9 + 16 – 12 = 25 – 12 = 13.

BC = √13 cm.

Let’s find the area of the triangle ABC:

S = (1/2) * AB * AC * sinA = (1/2) * 3 * 4 * sin60 = (1/2) * 12 * (√3 / 2) = 6 * (√3 / 2) = 3√3 (cm2).

Answer: the side BC is √13 cm, the area of the triangle ABC is 3√3 cm2.