Calculating the Length of a Side in Triangle Using Law of Cosines

In triangle ABC, the lengths of sides AB and AC are 8 cm and 6 cm, respectively. The angle at vertex A, denoted as θ, is 45 degrees. To find the length of side BC, apply the Law of Cosines, which is expressed as:

$$c^2 = a^2 + b^2 - 2ab imes ext{cos}( heta)$$

where:

• c is the length of side BC
• a is the length of side AB
• b is the length of side AC
• θ is the angle at vertex A

Calculate the length of side BC.