Question 1: Rewrite the Cosine Rule formula to make the angle A the subject, given sides a, b, and c.

Answer: cos A = (b^2 + c^2 - a^2) / (2bc)

Question 2: Given sides b=7, c=10, and angle A=60°, calculate side a using the rearranged Cosine Rule.

Answer: 10.2

Question 3: A triangle has sides a=8, b=6, and included angle C=45°. Rearrange the cosine rule to find side c.

Answer: c^2 = 8^2 + 6^2 - 2×8×6×cos 45°

Question 4: Fluency & Practice: Rearrange the formula to find cos B when sides a=9, c=12, and side b is unknown.

Answer: cos B = (a^2 + c^2 - b^2) / (2ac)

Question 5: Use the rearranged formula to find angle C given sides a=5, b=7, c=8.

Answer: 50.4°

Question 6: Problem Solving & Reasoning: A triangle has sides a=10, b=14, and angle C=65°. Rearrange the Cosine Rule to find side c, then calculate its length.

Answer: c ≈ 15.4

Question 7: In a real-world context, a surveyor measures two sides of a triangle as 20m and 25m with an included angle of 70°. Rearrange the formula to find the third side.

Answer: ≈33.5 meters

Question 8: Challenge & Extension: Derive an expression for angle A in terms of sides a, b, and c, starting from the cosine rule.

Answer: A = arccos[(b^2 + c^2 - a^2) / (2bc)]

Question 9: Mixed Review: Given sides a=6, b=8, and side c=10, rearrange the cosine rule to find angle B and calculate its value.

Answer: ≈53.13°

Question 10: Error Analysis: A student rearranged the cosine rule incorrectly as cos A = (a^2 + b^2 - c^2) / (2ab). Identify the mistake and correct the formula.

Answer: Incorrect because the formula should be cos A = (b^2 + c^2 - a^2) / (2bc); the sides must be opposite the angles used.

Question 11: Construct a triangle with sides 9, 12, and 15, and determine the size of the angle opposite the side of length 15 by rearranging the cosine rule.

Answer: ≈37°