Topic 6.2 – The Sine Rule

In $\triangle ABC$, $a = 8$, $A = 40^\circ$, $B = 60^\circ$. Find $b$ using the sine rule.

The sine rule is given as:

In $\triangle PQR$, $PQ = 10$, $PR = 12$, $\angle QPR = 40^\circ$, $\angle PQR = 75^\circ$. Find $QR$.

In $\triangle XYZ$, $x = 5$, $y = 7$, $\angle X = 40^\circ$. Find $\angle Y$.

In $\triangle LMN$, $l = 9$, $m = 12$, $\angle L = 40^\circ$. Find $\angle M$.

A triangle has sides $a = 7$, $b = 9$, and $\angle A = 40^\circ$. Find $\angle B$.

Which of the following is not a correct use of the sine rule?

In a triangle, $A = 50^\circ$, $B = 70^\circ$, $a = 8$. Find $b$.

In $\triangle ABC$, $a = 12$, $A = 45^\circ$, $C = 85^\circ$. Find $c$.

The sine rule can be applied to: