39º
1) Considering what's been given we can sketch this out:
From these trees leaning on each other, we can visualize a triangle (in black).
2) So now, since we need to find the other angle, then we need to apply the Law of Sines to find out the missing angle:
[tex]\begin{gathered} \frac{a}{\sin(A)}=\frac{b}{\sin (B)} \\ \frac{16}{\sin(32)}=\frac{19}{\sin (X)} \\ 16\cdot\sin (x)=19\cdot\sin (32) \\ \frac{16\sin(X)}{16}=\frac{19\sin (32)}{16} \\ \sin (X)=\frac{19\sin(32)}{16} \\ \end{gathered}[/tex]As we need the measure of the angle, (not any leg) then we need to use the arcsine of that quotient:
[tex]\begin{gathered} X=\sin ^{-1}(\frac{19\cdot\sin (32)}{16}) \\ X=38.996\approx39 \end{gathered}[/tex]3) Hence, the approximate measure of that angle X is 39º
