Question 1: Given a triangle with sides a=7 cm, b=10 cm, and angle A = 40°, use the sine rule to find angle B. Show your calculations.

Answer: Answer based on calculation

Question 2: In a triangle, sides are a=8 cm, b=12 cm, and angle A=30°. Determine whether the sine rule will give one solution, two solutions, or no solution for angle B.

Answer: Two solutions / One solution / No solution

Question 3: Calculate the possible values of angle B when given sides a=5 cm, b=9 cm, and angle A=60°, considering the ambiguous case.

Answer: Answer based on calculation

Question 4: If the sine rule produces two possible angles for B in a triangle with given sides, explain how you determine which is the correct angle in a real-world context.

Answer: Explanation of context-based decision

Question 1: A ship is sailing towards a lighthouse. The angles of elevation from two points 150 m apart are 35° and 50°. Assuming the lighthouse is directly behind the second point, find the height of the lighthouse. Consider the ambiguous case when applying the sine rule.

Answer: Solution with explanation

Question 2: Given sides a=6 cm, b=10 cm, and an unknown angle A, determine all possible angles B if the triangle is ambiguous. Explain how the sine rule leads to multiple solutions and which is valid based on the context.

Answer: Answer with explanation

Question 1: A drone pilot needs to determine the angle at which to tilt the drone to reach a target located 150 meters away, given certain side measurements. If two possible angles satisfy the sine rule ambiguity, explain how the pilot might decide which angle is appropriate. Provide calculations if necessary.

Answer: Decision explanation with calculations

Question 1: Construct a triangle with sides a=9 cm, b=14 cm, and an angle A=55°. Using the sine rule, determine all possible angles for B and discuss the conditions under which the ambiguous case occurs.

Answer: Constructed solution with explanation

Question 2: Consider a scenario where two triangles satisfy the same side lengths and one angle, but differ in the other angles due to the ambiguous case. Describe how you would verify which triangle is valid in a real-world setting.

Answer: Verification process explanation

Question 1: A student applies the sine rule to find angle B and concludes there is only one possible solution. Identify a common mistake that leads to this misconception and explain how to correctly determine the number of solutions.

Answer: Explanation of mistake and correction

Question 2: Given a set of side lengths and angles, a student finds two possible angles for B but only reports one. Explain why both solutions are valid in the ambiguous case and how to present both in your answer.

Answer: Explanation of both solutions' validity