Question 1: Construct a triangle where one side measures 6 cm, the adjacent side measures 8 cm, and the included angle is 60°. Use the grid to draw accurately.

Answer: Constructed triangle with specified sides and angle.

Question 2: Calculate the length of the third side of the triangle constructed in Question 1 if the included angle is 60°.

Answer: 10 cm

Question 3: In a construction, two sides measure 5 cm and 7 cm with an included angle of 45°. Draw this triangle on the grid.

Answer: Constructed triangle with sides 5 cm, 7 cm, and included 45° angle.

Question 4: Using the same construction as Question 3, calculate the length of the third side.

Answer: 8.3 cm (approximate)

Question 5: A carpenter needs to construct a triangular frame with sides 10 cm and 14 cm, with an included angle of 75°. Draw the triangle accurately.

Answer: Constructed triangle fitting the specifications.

Question 6: Calculate the length of the third side of this triangle if the included angle is 75°.

Answer: 16.8 cm (approximate)

Question 7: Construct a triangle with sides 4 cm and 9 cm, and an included angle of 30°. Use the grid to draw precisely.

Answer: Constructed triangle with specified sides and angle.

Question 8: Find the length of the third side of the triangle from Question 7, given the included angle of 30°.

Answer: 10.2 cm

Question 9: A builder designs a triangular support with sides 12 m and 16 m, and an included angle of 45°. Draw this triangle accurately and find the length of the third side.

Answer: Constructed triangle; third side approximately 20.2 m.

Question 10: A common mistake is to forget to include the angle when constructing the triangle. Identify a mistake a student might make in constructing the triangle with sides 6 cm, 8 cm, and angle 60°, and explain how to avoid it.

Answer: Mistake: Drawing sides without setting the correct included angle; fix by accurately measuring and constructing the angle before drawing sides.

Question 11: Using the grid, construct a triangle with sides 7 cm and 9 cm, and an included angle of 45°. Then, calculate the third side length to check your construction.

Answer: Third side approximately 12.6 cm.

Question 12: Challenge: Given a triangle with sides 8 cm and 10 cm and an included angle of 60°, construct the triangle and verify your result by calculation. How does the Law of Cosines support your construction?

Answer: Constructed triangle; Law of Cosines confirms the third side is about 14.1 cm, validating the construction.