Sine Law Ambiguous Case Worksheet

Sine Law Ambiguous Case

Read each question carefully and show all your work. Round all answers to one decimal place unless otherwise specified.

1. The ambiguous case of the Sine Law occurs when we are given two   and an angle   one of them (SSA).

2. In the ambiguous case, there can be  ,  , or   possible triangles.

3. If the given angle is acute, and the side opposite the angle is   than the height but   than the adjacent side, there are two possible triangles.

4. In triangle ABC, if angle A = 30°, side a = 6, and side b = 10, how many possible triangles can be formed?

5. Which of the following conditions guarantees a unique triangle when using the Sine Law (SSA case)?

6. In ΔPQR, ∠P = 40°, p = 8 cm, and q = 10 cm. Determine the number of possible triangles and find all possible values for ∠Q.

7. A surveyor measures a triangular plot of land. They find that one side is 120 m long, an adjacent side is 150 m long, and the angle opposite the 120 m side is 55°. Calculate all possible lengths for the third side of the plot.

8. If the given angle in an SSA case is obtuse, there will always be two possible triangles.