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.

Answer: 50.2

Question 2: A triangle has sides a = 8 cm, b = 12 cm, and angle A = 45°. Find side b using the sine rule.

Answer: 14.6

Question 3: Calculate the length of side a in a triangle where b = 9 cm, angle A = 60°, and angle B = 45°. Use the sine rule.

Answer: 7.2

Question 4: In a triangle, sides a = 5 cm, b = 8 cm, and angle A = 40°. Find angle B using the sine rule.

Answer: 63.7

Question 5: A surveyor measures two sides of a triangular plot: 15 m and 20 m, with the included angle of 60°. Find the third side using the sine rule.

Answer: 23.2

Question 6: Construct a triangle with sides a = 6 cm, b = 9 cm, and angle A = 50° on the grid. Use the sine rule to verify the length of side b.

Answer: 9.0

Question 7: A ship sights two landmarks, 50 km apart. The angles observed from the ship are 30° and 45° respectively. If the ship is directly opposite one landmark, find its distance to that landmark using the sine rule.

Answer: 38.7

Question 8: Use the sine rule to find side a in a triangle where b = 11 cm, angle A = 35°, and angle B = 60°.

Answer: 14.2

Question 9: In triangle ABC, sides b and c are 9 cm and 13 cm respectively. Angle A is 40°. Find side a using the sine rule.

Answer: 8.4

Question 10: A parallelogram is inscribed in a triangle with sides 10 cm and 14 cm, with an angle of 70°. Find the length of the diagonal using the sine rule.

Answer: 18.4

Question 11: An error is made in applying the sine rule: a student swaps sides and angles. Identify and correct the mistake in this statement: 'a/sinA = b/sinB, with a=8, A=30°, and B=60°.'

Answer: Incorrect because the sides a and b are opposite angles A and B; swapping without considering which side is opposite which angle is wrong.