Answer
$a\approx40\ m$, $B\approx41^\circ$, $C\approx79^\circ$
Work Step by Step
1. Given $A=60^\circ, b=30\ m, c=45\ m$, use the Law of Cosines, we have:
$a^2=b^2+c^2-2bc\ cosC=30^2+45^2-2(30)(45)cos60^\circ=1575$ and $a=\sqrt {1575}\approx40\ m$
2. Use the Law of Sines, we have $\frac{sinB}{30}=\frac{sin60^\circ}{40}$ which gives $sinB\approx0.6495$ and $B=asin(0.6495)\approx41^\circ$
3. $C\approx180^\circ-60^\circ-41^\circ=79^\circ$
