Trigonometry Problem With Scaling

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

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  

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

\[tan70=\frac{OB}{OD} \rightarrow OD=\frac{OB}{tan70}=0.0975\]

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

Add comment

Security code