AHSME 1980 Problem 23

Line segments drawn from the vertex opposite the hypotenuse of a right triangle to the points trisecting the hypotenuse have lengths $\sin x$ and $\cos x$, where $x$ is a real number such that $0<x<\frac{\pi}{2}$. The length of the hypotenuse is $\text{(A)} \ \frac{4}{3} \text{(B)} \ \frac{3}{2} \text{(C)} \ \frac{3\sqrt{5}}{5} \text{(D)}\ \frac{2\sqrt{5}}{3} \text{(E)}\ \text{not uniquely determined}$