Sine Law Ambiguous Case Worksheet
Explore the ambiguous case of the Sine Law with various triangle scenarios and problem-solving exercises for Grade 10 students.
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Sine Law Ambiguous Case
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Read each question carefully and show all your work. Round your answers to one decimal place where necessary.
1. In your own words, explain what the 'ambiguous case' of the Sine Law refers to and when it occurs.
2. For triangle ABC, if side a = 10 cm, side b = 15 cm, and angle A = 30°, how many possible triangles can be formed?
Zero triangles
One triangle
Two triangles
Cannot be determined
3. The ambiguous case of the Sine Law occurs when you are given two and a non-included .
4. For an acute angle A, if a < h (where h is the from B to AC), then triangles can be formed.
5. Consider a triangle ABC where a = 8 cm, b = 12 cm, and angle A = 35°. Determine the number of possible triangles and find all possible values for angle B if a triangle exists.
6. If angle A is obtuse, and side a is greater than side b, then there is always one unique triangle.
True
False
7. A surveyor measures two sides of a triangular plot of land to be 75 meters and 100 meters. The angle opposite the 75-meter side is 40°. Find all possible lengths for the third side of the plot.
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