a/sinA = b/sinB: Error Analysis & Misconceptions
Mathematics
Year 9
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding, applying, and correcting misconceptions related to the formula a/sinA = b/sinB in triangles. Designed to develop procedural skills and reasoning in context.
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a/sinA = b/sinB: Error Analysis & Misconceptions
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Review the key formula a/sinA = b/sinB and its correct application in solving triangles. Pay attention to common mistakes in calculation and reasoning.
B
Fluency & Practice
Answer the following questions to practice applying the Sine Rule accurately.
1.
Given a triangle with sides a=8 cm, b=10 cm, and angle A=30°, find angle B using the Sine Rule.
[3 marks]2.
If a = 12 and A = 45°, and b = 15, what is the value of sinB? Round to two decimal places.
[2 marks]3.
Calculate side b in a triangle where a=9 cm, A=40°, and B=60°.
[3 marks]C
Problem Solving & Reasoning
Apply reasoning to multi-step problems involving the Sine Rule, explaining each step.
1.
A triangle has sides a=7 cm, b=9 cm, and angle A=50°. Find angle B and explain your method.
[4 marks]2.
Explain why using the Sine Rule incorrectly might lead to an impossible triangle. Provide an example scenario.
[3 marks]D
Real-world Applications
Solve the following contextual problems involving the Sine Rule.
1.
A surveyor measures two sides of a triangular plot: 50 m and 70 m, with the included angle 60°. Find the third side.
[3 marks]E
Challenge & Extension
Attempt these more difficult problems to deepen your understanding.
1.
Given a triangle with sides a=13, b=14, and angle A=70°, find the possible values for angle B. Discuss any ambiguities.
[4 marks]2.
Prove that if two triangles have the same ratio a/sinA = b/sinB, then they are similar. Include possible misconceptions.
[4 marks]F
Mixed Review & Error Analysis
Identify and correct the errors in the following student solutions.
1.
A student calculates sinB = (b × sinA)/a but forgets to check if sinB > 1. Explain why this is a mistake and what it indicates.
[3 marks]2.
A student uses the Sine Rule with angle A=45°, a=10, and b=16, but gets an impossible value for angle B. Identify the mistake.
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet