Let's take a look at the situation:
We know, because of the Pythagorean theorem, that:
[tex]\begin{gathered} d^2=45^2+36^2\rightarrow d=\sqrt[]{45^2+36^2} \\ \rightarrow d=57.63 \end{gathered}[/tex]Thereby, using the law of sines:
[tex]\begin{gathered} \frac{d}{\sin90}=\frac{45}{\sin a} \\ \rightarrow d\sin a=45\sin 90\rightarrow\sin a=\frac{45}{d} \\ \rightarrow a=\arcsin (\frac{45}{57.63}) \\ \rightarrow a=51.34 \end{gathered}[/tex]The angle of the bird's view on the worm is 51.34°
