1980 AHSME 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} \qquad \text{(B)} \ \frac{3}{2} \qquad \text{(C)} \ \frac{3\sqrt{5}}{5} \qquad \text{(D)}\ \frac{2\sqrt{5}}{3}\qquad \text{(E)}\ \text{not uniquely determined}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.