Given:
In a right triangle,
The opposite side is
[tex]8\sqrt[]{2}\text{ inches}[/tex]
The angle is 45 degrees.
To find the length of the hypotenuse side:
Using the trigonometric ratio,
[tex]\begin{gathered} \sin \theta=\frac{Opp}{\text{Hyp}} \\ \sin 45^{\circ}=\frac{8\sqrt[]{2}}{Hyp} \\ \frac{1}{\sqrt[]{2}}=\frac{8\sqrt[]{2}}{Hyp} \\ \text{Hyp}=8\sqrt[]{2}\times\sqrt[]{2} \\ \text{Hyp}=16\text{ inches} \end{gathered}[/tex]
Hence, the length of the hypotenuse side is 16 inches.
