Sine Law Ambiguous Case Worksheet

Sine Law Ambiguous Case Worksheet

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. The ambiguous case of the Sine Law occurs when we are given   side(s) and   angle(s), specifically a   case.

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

3. To determine the number of possible triangles, we compare the height (h) to the given side opposite the angle (a) and the adjacent side (b). If a < h, there are   triangles.

4. If a > b, there is   triangle.

1. For triangle ABC, given A = 30°, b = 10 cm, and a = 7 cm. Determine the number of possible triangles. Show your calculations.

2. Explain why the Sine Law can lead to an ambiguous case.

1. In triangle PQR, if p = 8 cm, q = 12 cm, and ∠P = 30°, how many unique triangles can be formed?

2. Which of the following conditions guarantees a unique triangle when using the Sine Law?

1. If the given angle is obtuse, the Sine Law will always result in an ambiguous case.

2. In the ambiguous case, if a = h, there is exactly one possible triangle (a right-angled triangle).

1. Consider a triangle with angle A = 45°, side a = 6 cm, and side b = 8 cm. Find all possible values for angle B and angle C. Round to one decimal place.

2. A triangle has sides x, y, and z. Given that ∠X = 60°, y = 10 units, and x = 9 units. Determine if there is an ambiguous case and find the possible values for ∠Y. Round to one decimal place.