Suppose we have the problem below, in which it is required to find the angle  {jatex options:inline}x{/jatex}.

Put as much information on the diagram as possible. If we scale the diagram, all the angles will remain the same. Scale the diagram so that  {jatex options:inline}AO=1{/jatex}.

Now we can use some trigonometry. Use the Sine Rule to calculate  {jatex options:inline}OB{/jatex}  and  {jatex options:inline}OE{/jatex}.
{jatex options:inline}\frac{OC}{sin30}=\frac{1}{sin60} \rightarrow OC=\frac{sin30}{sin60} \times 1 =0.5774{/jatex} {jatex options:inline}\frac{OB}{sin15}=\frac{1}{sin75} \rightarrow OB=\frac{sin15}{sin75} \times 1 =0.2679{/jatex}

Then  {jatex options:inline}tan70=\frac{OB}{OD} \rightarrow OD=\frac{OB}{tan70}=0.0975{/jatex}

Finally  {jatex options:inline}tanx=\frac{OD}{OC}=\frac{0/0975}{02679}=0/1689 \rightarrow x=tan^{-1}(0.1689)=9.59^o{/jatex}  to 3 significant figures.
Note that all the working is to 4 significant figures, and the final answer to to 1 less significant figure.