B ΔABC, side AB = 8 cm, angle C = 30 °, angle A = 45 °. Find the BC side.

In triangle ABC it is known:

AB = 8 cm,

Angle C = 30 °;

Angle A = 45 °.

Let’s find the side of the BC.

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

AB / sin C = BC / sin A;

Substitute the known values and calculate the BC side of the ABC triangle.

8 / sin 30 ° = BC / sin 45 °;

BC * sin 30 ° = 8 * sin 45 °;

BC * 1/2 = 8 * √2 / 2;

BC * 1/2 = 4√2;

Let’s multiply the values cross by a cross and get rid of the fraction.

BC = 2 * 4√2;

BC = 8√2;

As a result, we got that the side of the triangle is BC = 8√2.