In a triangle ABC AB = 6cm, angle A = 45 degrees, angle C = 120 degrees. Find the BC side.

In the ABC triangle it is known:

AB = 6 cm;

Angle A = 45 °;

Angle C = 120 °.

Let’s find the side of the BC.

In order to find the side of the BC, we apply the sine theorem.

BC / sin A = AB / sin C;

Substitute the known values and calculate the BC side.

BC / sin 45 = 6 / sin 120;

BC / (√2 / 2) = 6 / (√3 / 2);

BC * 2 / √2 = 6 * 2 / √3;

BC / √2 = 6 / √3;

BC * √3 = 6 * √2;

BC = 6 * √2 / √3;

BC = 6√ (2/3).

This means that the side of the triangle ABC is equal to BC = 6√ (2/3).