## Trigonometry Problem With Scaling

Suppose we have the problem below, in which it is required to find the angle
$x$
.

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
$AO=1$
.

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

Then
$tan70=\frac{OB}{OD} \rightarrow OD=\frac{OB}{tan70}=0.0975$

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