Question 1: Given a triangle with sides a = 7 cm, b = 10 cm, and angle A = 30°, use the Sine Rule to find angle B. State whether the ambiguous case applies.

Answer: Answer with angle B in degrees and note if two solutions exist

Question 2: A triangle has sides of 8 cm and 12 cm with an included angle of 45°. Find the possible angles opposite the sides using the Sine Rule.

Answer: Two possible angles, approximately 23.4° and 156.6°

Question 3: In a triangle, side a = 9 cm, side b = 6 cm, and angle A = 60°. Calculate angle B and determine if there is an ambiguity.

Answer: Angle B approximately 35.3°; no ambiguity since only one solution

Question 4: A triangle has sides 5 cm and 9 cm with an angle of 70°. Use the Sine Rule to find the possible measures of the opposite angles. Explain your reasoning.

Answer: Two possible angles, approximately 20.4° and 139.6°, due to the ambiguous case

Question 5: Construct a triangle where side a = 6 cm, side b = 10 cm, and angle A = 40°. Show all steps and state whether the triangle is unique or possible in two configurations.

Answer: Constructed triangle with two possible solutions or one, depending on the case

Question 6: A surveyor measures two sides of a triangle as 15 m and 20 m with an included angle of 50°. Find the possible angles opposite the measured sides, discussing the ambiguity.

Answer: Two possible angles, approximately 41.8° and 138.2°

Question 7: Explain why the ambiguous case occurs in the Sine Rule and give an example scenario where it might arise.

Answer: When two sides and a non-included angle are known, and the given side length allows for two solutions due to the sine function's properties

Question 8: Given side a = 8 cm, side b = 15 cm, and angle A = 60°, find all possible solutions for angle B, showing your calculations.

Answer: Angles approximately 29.5° and 150.5°, indicating the ambiguous case

Question 9: Identify and explain common mistakes students make when solving ambiguous case problems with the Sine Rule, and how to avoid them.

Answer: Common mistakes include assuming only one solution, misapplying the sine inverse, or forgetting to check for the second possible solution

Question 10: A triangle with sides 9 cm and 13 cm has an included angle of 55°. Use the Sine Rule to find the possible measures of the opposite angles, considering the ambiguous case.

Answer: Angles approximately 22.8° and 157.2°