we are given
[tex] opposite=5\sqrt{2} [/tex]
[tex] \theta=45 [/tex]
[tex] hypotenuse=c [/tex]
now, we can use sine formula
[tex] sin(\theta)=\frac{5\sqrt{2}}{c} [/tex]
now, we can plug theta
[tex] sin(45)=\frac{5\sqrt{2}}{c} [/tex]
now, we can find c
[tex] c=\frac{5\sqrt{2}}{sin(45)} [/tex]
[tex] c=\frac{5\sqrt{2}}{\frac{\sqrt{2}}{2}} [/tex]
now, we can simplify it
[tex] c=\frac{5*2*\sqrt{2}}{\sqrt{2}} [/tex]
[tex] c=10 [/tex]............Answer
