To find the value of the missing side we can use the trigonometric functions with the values of tha angle and the side given because its a righ triangle.
The corresponding trigonometric is the sin of 82° which involves the opposite side of the angle (x) and the hypotenuse
[tex]\begin{gathered} \sin 82=\frac{x}{\text{hyp}} \\ \sin 82=\frac{x}{3.4} \\ x=3.4\sin 82 \\ x=3.3669 \\ x\cong3.4ft \end{gathered}[/tex]