Law of Cosines Worksheet

Law of Cosines Worksheet

Read each question carefully and solve for the unknown side or angle using the Law of Cosines. Round your answers to two decimal places.

1. In triangle ABC, given a = 10, b = 12, and C = 60°. Find the length of side c.

2. A triangle has sides of length p = 7 cm, q = 9 cm, and the angle between them is R = 100°. Find the length of side r.

3. In triangle XYZ, sides are x = 8, y = 15, and z = 12. Find the measure of angle X.

4. A triangle has sides of length a = 5 km, b = 7 km, and c = 10 km. Find the measure of angle B.

5. The Law of Cosines is used to find missing sides or angles in a triangle when you have SSS (Side-Side-Side) or SAS (Side-Angle-Side) information. The formula for finding side 'a' is a² = b² + c² - 2bc  .

6. To find an angle, say angle C, when all three sides (a, b, c) are known, the formula is cos C = (a² + b² - c²) /  .

7. The Law of Cosines can be used for right-angled triangles as well as non-right-angled triangles.

8. If you are given two angles and one side (AAS or ASA), you should use the Law of Cosines to solve the triangle.