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1980 AMC 12 Question 23

AMC12 · 1980 AMC 12

Question 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 $0\lt x\lt\frac\pi2.$ The length of the hypotenuse is
  1. $\frac43$
  2. $\frac32$
  3. $\frac{3\sqrt5}{5}$
  4. $\frac{2\sqrt5}{3}$
  5. not uniquely determined by the given information