Triangle ABC AC = 10cm AB = 5cm angle BAC = 60 degrees BC-?

Knowing the two sides of the triangle and the angle between them, we can find the third side through the cosine.

Cosine theorem: a ^ 2 = b ^ 2 + c ^ 2 – 2bc * cosα (the square of the side of the triangle is equal to the sum of the squares of the other two sides minus the double product of these sides and the cosine of the angle between them).

BC ^ 2 = AC ^ 2 + AB ^ 2 – 2 * AC * AB * cosBAC

BC ^ 2 = 10 ^ 2 + 5 ^ 2 – 2 * 10 * 5 * cos60∘ = 100 + 25 – 100 * 1/2 = 125 – 50 = 75

BC = √75 = √25 * √3 = 5√3 (Remember that the number under the root can be represented as a product, and √a * b = √a * √b).

Answer: BC = 5√3 cm.