You can use the sine law, which states that, in every triangle, the ratio between a side and the sine of the opposite angle is constant.
So, we have
[tex]\dfrac{59}{\sin(90)}=\dfrac{42}{\sin(x)}[/tex]
where [tex]x[/tex] is the angle you're looking for. Now, remember that [tex]\sin(90)=1[/tex], and we can solve the equation for [tex]\sin(x)[/tex]:
[tex]\sin(x)=\dfrac{42}{59}[/tex]
Which implies that the angle itself is
[tex]x=\arcsin\left(\dfrac{42}{59}\right)\approx 45.39[/tex]
