a² = b² + c² - 2bc cosA: Error Analysis & Misconceptions
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
This worksheet explores common errors and misconceptions when applying the Cosine Rule a² = b² + c² - 2bc cosA, focusing on identifying and correcting mistakes in calculations and understanding.
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a² = b² + c² - 2bc cosA: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show detailed working in the grid spaces provided.
1.
Calculate side a in a triangle where b = 7 cm, c = 9 cm, and angle A = 60°. Use the Cosine Rule: a² = b² + c² - 2bc cosA.
[3 marks]2.
Given b = 5, c = 12, and angle A = 45°, find side a using the Cosine Rule.
[3 marks]3.
If a triangle has sides b = 8 and c = 6, and angle A is 90°, what is side a? (Hint: recall that cos90°=0).
[2 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems. Explain your reasoning clearly.
1.
A triangle has sides b = 10 cm, c = 15 cm, and angle A = 75°. Calculate side a. Then, explain what mistake might occur if a student incorrectly uses the formula a² = b² + c² + 2bc cosA.
[4 marks]2.
A triangle has side a = 9 cm, side c = 14 cm, and angle A = 30°. Find side b. Describe the steps you take and any assumptions made.
[4 marks]C
Real-world Applications
Apply the Cosine Rule to solve these practical problems.
1.
A surveyor measures two sides of a triangular plot as 50 m and 60 m, with the included angle as 70°. Find the length of the third side to determine the boundary.
[3 marks]2.
In a construction project, two beams are connected at an angle of 45°, with lengths 8 m and 10 m. Calculate the distance between their endpoints.
[3 marks]D
Challenge & Extension
Tackle these advanced problems to deepen your understanding.
1.
Prove that if two sides of a triangle are equal and the included angle is 120°, then the third side can be found using the Cosine Rule. Use specific numbers: b=c=10, angle A=120°.
[3 marks]2.
A triangle has sides b = 7, c = 9, but the student mistakenly applies a² = b² + c² + 2bc cosA. Identify the error, correct the formula, and recalculate side a.
[4 marks]E
Mixed Review
Answer these varied questions to consolidate your understanding.
1.
Construct a triangle with sides 6 cm, 8 cm, and an included angle of 60°. Use the grid to draw and verify the side length.
[2 marks]2.
Plot the graph of y=2x and mark a point corresponding to x=5. How does this relate to side b in the Cosine Rule?
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet