Law of Sines Mastery

Law of Sines Mastery

Read each question carefully and use the Law of Sines to solve for the unknown side or angle. Show all your work.

1. In triangle ABC, angle A = 45°, angle B = 60°, and side a = 10 cm. Find the length of side b.

2. In triangle PQR, angle P = 75°, angle Q = 40°, and side q = 12 inches. Find the length of side p.

3. In triangle XYZ, angle X = 50°, side x = 8 cm, and side y = 10 cm. Find the measure of angle Y to the nearest degree.

4. In triangle DEF, angle D = 30°, side d = 7 units, and side e = 14 units. Find the measure of angle E to the nearest degree. (Be aware of the ambiguous case!)

5. Which of the following conditions is NOT suitable for applying the Law of Sines?

6. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle   that side is the same for all three sides of the triangle.

7. The ambiguous case (SSA) for the Law of Sines can result in  , one, or no possible triangles.

8. A surveyor wants to find the distance between two points, A and B, on opposite sides of a river. They stand at a point C, 100 meters from A. From C, the angle to A is 70° and the angle to B is 50°. Find the distance between A and B.