Answer
$63.7$
Work Step by Step
Let c be the shared side.
In the triangle with the given acute angle of $60^{o}$,
c is the hypotenuse, 50 is the side opposite the angle.
$\displaystyle \sin 60^{o}=\frac{50}{c}\ \Rightarrow\ c=\frac{50}{\sin 60^{o}}$
In the triangle with the given acute angle of $65^{o}$,
c is the leg opposite the angle, x is the hypotenuse
$\displaystyle \sin 65^{o}=\frac{c}{x}\ \Rightarrow\ x=\frac{c}{\sin 65^{o}}=\frac{50}{\sin 60^{o}\sin 65^{o}}$
$\approx$63.7035538531
$x\approx 63.7$
