The Sine Rule Flashcards

All 6 cards in this deck

State the sine rule in the form used to find a missing side.

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Each side is paired with the angle opposite it.

State the sine rule in the form used to find a missing angle.

$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

What are the steps to find a missing side using the sine rule?

e.g. find $x$, the side opposite $40^\circ$, when the side opposite $80^\circ$ is $10$ cm

1. Pair each side with its opposite angle: $\dfrac{x}{\sin 40^\circ}=\dfrac{10}{\sin 80^\circ}$
2. Multiply by $\sin 40^\circ$: $x=\dfrac{10\sin 40^\circ}{\sin 80^\circ}$
3. Evaluate: $x=6.53$ cm (3 s.f.)

What are the steps to find a missing angle using the sine rule?

e.g. find angle $B$, opposite $7$ cm, when the side opposite $30^\circ$ is $10$ cm

1. Use $\dfrac{\sin B}{b}=\dfrac{\sin A}{a}$: $\dfrac{\sin B}{7}=\dfrac{\sin 30^\circ}{10}$
2. Rearrange: $\sin B=\dfrac{7\sin 30^\circ}{10}=0.35$
3. Inverse sine: $B=\sin^{-1}(0.35)=20.5^\circ$ (1 d.p.)

True or false? In the sine rule, the side $a$ is the side next to angle $A$.

False.

$a$ is the side opposite angle $A$.

The sine rule gives $\sin x = 0.6$, and the diagram shows $x$ is obtuse. How do you obtain the obtuse angle?

Work out $180^\circ-\sin^{-1}(0.6)$.

The calculator only gives the acute solution.