Question 1: Rearrange the Cosine Rule formula to express cos C in terms of sides a, b, and c.

Answer: cos C = (a² + b² - c²) / (2ab)

Question 2: Given sides a=7, b=10, and angle C=60°, use the rearranged formula to find side c. Show all steps.

Answer: c ≈ 11.1

Question 3: Identify the mistake in the following rearrangement: cos C = (a² + b² + c²) / (2ab).

Answer: Incorrect sign; should be minus c², not plus c².

Question 4: Rewrite the formula used to find angle C when sides a, b, c are known, starting from the original Cosine Rule.

Answer: cos C = (a² + b² - c²) / (2ab)

Question 5: A triangle has sides a=8, b=15, and c=17. Rearrange the Cosine Rule to find angle C, and calculate its value.

Answer: C ≈ 28.1°

Question 6: Explain why improper rearrangement of the Cosine Rule might lead to incorrect angle calculations.

Answer: Incorrect signs, missing parentheses, or algebraic errors can lead to wrong results.

Question 7: Construct a triangle with sides 5, 12, and 13. Use the rearranged formula to find angle C opposite side c=13. Show your steps.

Answer: C ≈ 22.6°

Question 8: Identify and correct the error in this rearranged formula: cos C = (a² + c² - b²) / (2ac).

Answer: Error: The formula should be cos C = (a² + b² - c²) / (2ab); the numerator's last term incorrectly uses c².

Question 9: Solve for angle C using the sides a=9, b=12, c=15. Show all steps.

Answer: C ≈ 65.2°

Question 10: A student rearranged the Cosine Rule as cos C = (a² - b² + c²) / (2ac). Is this correct? Explain your reasoning.

Answer: No, the correct formula is cos C = (a² + b² - c²) / (2ab).

Question 11: Derive the formula for angle C starting from the original Cosine Rule, highlighting each step carefully.

Answer: Starting from c² = a² + b² - 2ab cos C, rearranged as cos C = (a² + b² - c²) / (2ab).