Sine Law Ambiguous Case Worksheet
Explore the ambiguous case of the Sine Law with various triangle scenarios and problem-solving exercises.
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Sine Law Ambiguous Case Worksheet
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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?
Zero
One
Two
Three
2. Which of the following conditions guarantees a unique triangle when using the Sine Law?
Given an acute angle and the side opposite is shorter than the height.
Given an acute angle and the side opposite is longer than the adjacent side.
Given an acute angle and the side opposite is equal to the height.
Given an obtuse angle and the side opposite is shorter than the adjacent side.
1. If the given angle is obtuse, the Sine Law will always result in an ambiguous case.
True
False
2. In the ambiguous case, if a = h, there is exactly one possible triangle (a right-angled triangle).
True
False
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.