1fully worked

In triangle $ABC$, $A=40^\circ$, $B=75^\circ$ and $a=8$ cm. Find $b$.

1$\dfrac{b}{\sin B}=\dfrac{a}{\sin A}$Write the sine rule for the pair

2$\dfrac{b}{\sin75^\circ}=\dfrac{8}{\sin40^\circ}$Substitute the known values

3$b=\dfrac{8\sin75^\circ}{\sin40^\circ}=12.0$ cmRearrange and evaluate (1 d.p.)

Check - Which side-angle pair lets us start?

A $a$ and $A$ – a side with its opposite angleB $b$ and $A$C $a$ and $B$D any two angles

2you finish it

In triangle $ABC$, $A=35^\circ$, $B=80^\circ$ and $a=6$ cm. Find $b$.

1$\dfrac{b}{\sin80^\circ}=\dfrac{6}{\sin35^\circ}$Write the sine rule for the pair

2$b=\dfrac{6\sin80^\circ}{\sin35^\circ}$Substitute the known values

3Rearrange and evaluate (1 d.p.)

Check - To make $b$ the subject you...

A add $\sin80^\circ$ to both sidesB multiply both sides by $\sin80^\circ$C divide by $6$D square both sides

3you finish it

In triangle $ABC$, $A=50^\circ$, $B=60^\circ$ and $a=10$ cm. Find $b$.

1$\dfrac{b}{\sin60^\circ}=\dfrac{10}{\sin50^\circ}$Write the sine rule for the pair

2Substitute the known values

3Rearrange and evaluate (1 d.p.)

Check - Why is $b$ bigger than $a$ here?

A a calculation errorB angle $B$ is bigger than angle $A$, so its opposite side is longerC sides are always increasingD because $60>50$ has no effect

4you do it all

In triangle $ABC$, $A=48^\circ$, $B=72^\circ$ and $a=9$ cm. Find $b$.

1Write the sine rule for the pair

2Substitute the known values

3Rearrange and evaluate (1 d.p.)

Check - What must the calculator be set to?

A radiansB degreesC gradiansD it does not matter