Given:
In the given 45-45-90 triangle,
Use the tan ratio,
[tex]\begin{gathered} \tan 45^{\circ}=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan 45^{\circ}=\frac{v}{7} \\ 1=\frac{v}{7} \\ v=7 \end{gathered}[/tex]
Use the cosine ratio,
[tex]\begin{gathered} \cos 45^{\circ}=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \cos 45^{\circ}=\frac{7}{u} \\ \frac{1}{\sqrt[]{2}}=\frac{7}{u} \\ u=\frac{7}{\sqrt[]{2}} \\ u=7\sqrt[]{2} \end{gathered}[/tex]
Answer: option a)
[tex]u=7\sqrt[]{2},v=7[/tex]
