Question 1: Given sides a=8 cm, b=10 cm, and included angle C=60°, calculate the area of the triangle.

Answer: 40√3 cm² or approximately 69.28 cm²

Question 2: Sides a=5 m, b=7 m, and C=45°. Find the area of the triangle.

Answer: 12.3 m² (approx)

Question 3: If side a=9 cm, side b=12 cm, and the area is 54 cm², find the included angle C.

Answer: C ≈ 45°

Question 1: Sides a=6 cm, b=8 cm, and angle C=60°. Calculate the area. Then, find the length of side c using the Law of Cosines.

Answer: Area ≈ 20.8 cm²; c ≈ 9.2 cm

Question 2: A triangle has sides 7 m and 9 m with an included angle of 120°. Find its area.

Answer: 37.8 m² (approx)

Question 1: A triangular plot of land has sides 50 m and 80 m with an included angle of 30°. Calculate the area of the land.

Answer: 1000 m² (approx)

Question 2: A surveyor measures two sides of a triangular boundary as 120 m and 150 m, with an included angle of 45°. Find the area enclosed.

Answer: 11,250 m² (approx)

Question 1: Given two sides a=9 cm and b=14 cm with an included angle C=70°, find the area and then determine the length of side c using the Law of Cosines. Explain your steps.

Answer: Area ≈ 69.4 cm²; c ≈ 16.2 cm

Question 2: Construct a triangle on the grid with sides 6 cm and 8 cm meeting at an angle of 120°. Calculate its area and verify your construction.

Answer: Area ≈ 18.5 cm²

Question 1: A student calculates the area of a triangle with sides 10 cm, 12 cm, and included angle 90° as 60 cm². Identify and explain the mistake.

Answer: Misused the formula for right-angled triangle or used incorrect angle.

Question 2: A triangle has sides 7 cm, 9 cm, and an included angle of 60°. A student calculates the area as 27 cm². Check if this is correct and justify your answer.

Answer: Incorrect; actual area ≈ 27.7 cm², student slightly underestimated.