We will have the following:
We first determine "b", that is:
[tex]\begin{gathered} b=\sqrt{42766^2-35276^2}\Rightarrow b=24177.14996... \\ \\ \Rightarrow b\approx24177 \end{gathered}[/tex]
Now, using the law of sines we determine the measure of the angles, that is:
alpha:
[tex]\begin{gathered} \frac{sin(\alpha)}{35276}=\frac{sin(90)}{42766}\Rightarrow sin(\alpha)=\frac{35276}{42766} \\ \\ \Rightarrow\alpha=sin^{-1}(\frac{35276}{42766})\Rightarrow\alpha=55.5743883... \\ \\ \Rightarrow\alpha\approx55.574 \end{gathered}[/tex]
Beta:
[tex]\begin{gathered} \frac{sin(\beta)}{24177.14996}=\frac{sin(90)}{42766}\Rightarrow sin(\beta)=\frac{24177.14996}{42766} \\ \\ \Rightarrow\beta=sin^{-1}(\frac{24177.14996}{42766})\Rightarrow\beta=34.42561171... \\ \\ \Rightarrow\beta\approx34.426 \end{gathered}[/tex]
