First of all, recall the trigonometric identities
[tex]\sin (\theta)=\frac{O}{H}[/tex][tex]\cos (\theta)=\frac{A}{H}[/tex][tex]\tan (\theta)=\frac{O}{A}[/tex]Where O = Opposite side, A = Adjecent side and H = Hypotenuse side
First Triangle:
As you can see, we know the angle and the adjacent side and the opposite side is unknown (x)
[tex]\begin{gathered} \tan (32)=\frac{x}{13} \\ x=\tan (32)\cdot13 \\ x=0.62\cdot13 \\ x=8.1 \end{gathered}[/tex]Therefore, the opposite side is 8.1
Second Triangle:
As you can see, we know the angle (37) and the adjacent side and the hypotenuse side is unknown (x)
[tex]\begin{gathered} \cos (\theta)=\frac{A}{H} \\ \cos (37)=\frac{11}{x} \\ x=\frac{11}{\cos (37)} \\ x=\frac{11}{0.798} \\ x=13.9 \end{gathered}[/tex]Therefore, the hypotenuse side is 13.9
Third Triangle:
As you can see, the angle is unknown but the adjacent and opposite sides are given so we can use the tan identity.
[tex]\begin{gathered} \tan (\theta)=\frac{O}{A} \\ \tan (\theta)=\frac{4}{13} \\ \theta=\tan ^{-1}(\frac{4}{13}) \\ \theta=17.1 \end{gathered}[/tex]Therefore, the missing angle is 17.1