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### Sine Rule IB Math Studies

Posted: Mon Apr 15, 2013 7:21 pm
IB Mathematical Studies – Trigonometry, Sine Rule

How can we find the side $a$ of a triangle ABC given that $\hat{A}=30^{\circ} , c=6 \ and\ \hat{C}=60^{\circ}$ ?

Thanks!

### Re: Sine Rule IB Math Studies

Posted: Mon Apr 15, 2013 7:31 pm
IB Maths SL – Trigonometry, Sine Rule

The Sine rule states

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

So in your case the side $a$ can be calculated as follows:

$\frac{a}{sin30^{\circ}}=\frac{6}{sin60^{\circ}}$

$a=\frac{1}{2} \frac{6}{\frac{\sqrt 3}{2}}=\frac{6}{ \sqrt 3}$

Hope these help!!

### Re: Sine Rule IB Math Studies

Posted: Mon Apr 15, 2013 7:46 pm
Thanks Elisabeth!!