Since it is a right triangle, we can use the trigonometric ratio sin(θ).
[tex]\sin (\theta)=\frac{\text{ Opposite side}}{\text{Hypotenuse}}[/tex]
So, in this case, we have:
[tex]\begin{gathered} \theta=45\degree \\ \text{ Opposite side }=17 \\ \text{ Hypotenuse }=x \end{gathered}[/tex][tex]\begin{gathered} \sin (\theta)=\frac{\text{ Opposite side}}{\text{Hypotenuse}} \\ \sin (45\degree)=\frac{17}{x} \end{gathered}[/tex]
Now, we solve for x the above equation:
[tex]\begin{gathered} \text{Multiply by x from both sides} \\ \sin (45\degree)\cdot x=\frac{17}{x}\cdot x \\ x\sin (45\degree)=17 \\ \text{ Divide by }\sin (45\degree)\text{ from both sides} \\ \frac{x\sin(45\degree)}{\sin(45\degree)}=\frac{17}{\sin(45\degree)} \\ x=\frac{17}{\sin(45\degree)} \\ x=\frac{17}{\frac{1}{\sqrt[]{2}}} \\ x=\frac{\frac{17}{1}}{\frac{1}{\sqrt[]{2}}} \\ x=\frac{17\cdot\sqrt[]{2}}{1\cdot1} \\ x=\frac{17\sqrt[]{2}}{1} \\ $\boldsymbol{x=17\sqrt[]{2}}$ \end{gathered}[/tex]
Therefore, the value of x is:
[tex]$\boldsymbol{x=17\sqrt[]{2}}$[/tex]
