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by **Nyla** » Sun Aug 18, 2013 10:20 am

MYP Mathematics– Trigonometry, Sine Rule

How can we find the side $a$ of a triangle ABC given that $\hat{A}=30^{\circ} , c=8 \ and \hat{C}=60^{\circ}$ ?

Thanks!

by **Jack** » Sun Aug 18, 2013 10:27 am

MYP Mathematics Pre-diploma – 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:

$\frac{a}{sin30^{\circ}}=\frac{8}{sin60^{\circ}}$

$a=\frac{1}{2} \frac{8}{\frac{\sqrt 3}{2}}=\frac{8}{ \sqrt 3}$

Hope these help!!

by **Nyla** » Sun Aug 18, 2013 10:29 am

Thank you Jack.

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