Ambiguous Case: Fluency & Practice
Mathematics
Grade 6
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the Ambiguous Case of the Sine Rule, helping students develop procedural mastery and reasoning skills for different triangle configurations.
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Ambiguous Case: Fluency & Practice
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Given a triangle with side a = 7 cm, side b = 10 cm, and angle A = 40°, use the Sine Rule to find angle B. State whether there are one or two possible solutions.
[3 marks]2.
In a triangle, side a = 5 cm, side b = 8 cm, and angle A = 30°. Use the Sine Rule to determine possible values for angle B. Explain your reasoning.
[4 marks]3.
A triangle has sides a = 6 cm, b = 10 cm, and angle A = 60°. Is it possible for this triangle to have two different possible angles B? Justify your answer.
[3 marks]4.
Construct a triangle with side a = 4 cm, side b = 7 cm, and angle A = 50°, then use the Sine Rule to find angle B. Indicate how multiple solutions might occur.
[4 marks]5.
A surveyor measures side a = 9 m, side b = 12 m, and angle A = 70°. Determine if there are zero, one, or two possible solutions for angle B, and explain why.
[4 marks]6.
Given side a = 8 cm, side b = 5 cm, and angle A = 130°, find all possible angles B using the Sine Rule. How many solutions are there?
[3 marks]7.
A triangle has side a = 10 cm, side b = 15 cm, and angle A = 60°. Use the Sine Rule to find the possible angles B, considering the ambiguous case.
[4 marks]8.
A construction involves sides a = 6 cm, b = 9 cm, and angle A = 45°. After constructing the triangle, determine how many solutions exist for angle B and explain why.
[4 marks]9.
Solve for angle B if side a = 5 cm, side b = 8 cm, and angle A = 50°, and verify whether the ambiguous case applies.
[3 marks]10.
A triangle with side a = 7 cm, side b = 10 cm, and angle A = 35° shows two possible solutions for angle B. Calculate both and discuss how to determine if the second solution is valid in the context of the triangle.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet