Question 1: Construct triangle ABC where AB = 6 cm, AC = 4 cm, and the included angle BAC = 60°. Use the grid to accurately draw the triangle.

Answer: Constructed triangle with specified sides and included angle.

Question 2: Calculate the length of side BC in the triangle from Question 1, to 2 decimal places.

Answer: 7.21

Question 3: Construct a triangle with sides AB = 5 cm, AC = 7 cm, and included angle BAC = 45°. Confirm your construction by measuring the side BC.

Answer: Constructed triangle with side BC approximately 8.76 cm.

Question 4: In a triangle, sides AB = 8 cm, AC = 6 cm, and the included angle BAC = 75°. Use the cosine rule to find BC.

Answer: BC ≈ 9.52 cm

Question 5: A triangle has sides AB = 10 cm, AC = 7 cm, and included angle BAC = 30°. Calculate the area of the triangle.

Answer: Approximate area = 30.33 cm²

Question 6: Construct a triangle where AB = 4 cm, AC = 9 cm, and included angle BAC = 120°. Measure and record the length of side BC.

Answer: Constructed side BC approximately 11.68 cm.

Question 7: A triangle has sides AB = 7 cm, AC = 5 cm, and the included angle BAC = 90°. Use Pythagoras’ theorem to determine if the triangle is right-angled at B or C.

Answer: Right-angled at C

Question 8: Given a triangle with sides AB = 12 cm, AC = 5 cm, and included angle BAC = 60°, construct the triangle and then determine the length of BC.

Answer: BC ≈ 13.78 cm

Question 9: Identify and correct the mistake in constructing a triangle with sides 3 cm, 4 cm, and included angle 30°, where the student measures side BC as 5.5 cm.

Answer: Potential mistake: Incorrect angle or side measurement; correct by re-measuring and ensuring accurate construction.

Question 10: A real-world scenario: A surveyor constructs a triangle between two landmarks 8 km and 6 km apart, with the included angle at the first landmark being 45°. Using the cosine rule, estimate the distance between the second landmark and a third point such that the total triangle is completed.

Answer: Approximate third side ≈ 8.14 km

Question 11: Challenge: Construct a triangle with sides 7 cm and 9 cm, and included angle 135°. Use your construction to find the approximate length of the third side, then check your result with the cosine rule.

Answer: Third side ≈ 10.96 cm