Use the sine rule (ambiguous case is required), 𝑎 sin(𝐴) = 𝑏 sin(𝐵) = 𝑐 sin(𝐶), where 𝑎, 𝑏 and 𝑐 are the side lengths of the triangle and 𝐴, 𝐵 and 𝐶 are the corresponding opposite angles.

In triangle ABC, angle A is 35°, side b is 12 cm and side a is 8 cm. (a) Use the sine rule to calculate the size of angle B, correct to the nearest degree. (2 marks) (b) Explain whether a second possible value for angle B exists for this triangle. (2 marks)

Identify the possible values for angle R in the triangle shown.

A triangle has sides of length 7 cm and 9 cm, with an angle of 35° opposite the 7 cm side. Use the sine rule to find the angle opposite the 9 cm side, correct to the nearest degree. State both possible values.

In triangle ABC, \(a = 8\) cm, \(b = 12\) cm and \(\angle A = 35^\circ\). Explain why two different triangles can be constructed with these measurements.