Question 1: Construct a triangle with side lengths 5 cm and 7 cm, and an included angle of 60°. Use the grid to accurately draw the triangle. Then, verify the construction by measuring the sides.

Answer: Correctly constructed triangle with given sides and angle.

Question 2: You attempt to construct a triangle with sides 4 cm and 6 cm, and the included angle of 45°, but the sides do not meet when drawn. What common mistake might have caused this? Explain briefly.

Answer: Incorrect placement of sides or angle, or measurement errors.

Question 3: Given two sides of lengths 8 cm and 10 cm, and the included angle of 120°, use a calculator to find the length of the third side of the triangle using the Law of Cosines.

Answer: Approximately 12.65 cm

Question 4: In constructing a triangle with sides 3 cm and 4 cm, and the included angle of 90°, students notice the sides do not meet as expected. Identify and correct a common misconception that could lead to this issue.

Answer: Misjudging the angle measurement or misplacing the sides during construction.

Question 5: Construct a triangle with sides 6 cm and 9 cm and an included angle of 30°. Measure the third side and compare it with the value obtained from the Law of Cosines.

Answer: Approximately 9.97 cm

Question 6: Explain why constructing a triangle with sides 2 cm and 3 cm and an included angle of 10° might be difficult to do accurately without precise tools.

Answer: Small angle makes precise placement hard; sides are short, increasing measurement difficulty.

Question 7: Construct a triangle where two sides are 5 cm and 8 cm, and the included angle is 150°. Use the grid to aid your construction. Then, explain how the large angle affects the shape of the triangle.

Answer: Large angle causes the third side to be very short, making the triangle more elongated.

Question 8: A student constructs a triangle with sides 7 cm and 10 cm, and the included angle of 45°. They find the third side length to be 12 cm. Is this correct? Use the Law of Cosines to verify.

Answer: Approximately 11.70 cm; student's value is slightly overestimated.

Question 9: Identify a common error when students try to construct a triangle with side lengths 4 cm, 6 cm, and an included angle of 200°. Explain why this triangle cannot exist.

Answer: Triangle inequality fails; the sum of two sides is less than the third side or the angle is invalid.

Question 10: Construct a triangle with sides 3 cm and 7 cm, with an included angle of 90°. Then, use the Pythagorean theorem to find the length of the hypotenuse and compare with your construction.

Answer: Hypotenuse approximately 7.62 cm; construction should match this length.