In the triangle ABC, AB = 12 cm and AC = 10 cm, and ∠ BAC = 60°. What is the value of the length of the side BC ?

11.13 cm

We have a concept ,

According to the law of cosine, if a, b, and c are three sides of a triangle ΔABC and ∠A is the angle between AC and AB then, a² = b² + c² - 2bc × cos∠A

AB = 12 cm

AC = 10 cm,

∠BAC = 60°.

BC² = AB² + AC² - 2 × AB × AC × cos60°

= BC² = 12² + 10² - 2 × 12 × 10 × \(\frac{1}{2}\) 

= BC² = 124

= BC = 11.13