1980 AHSME Problems/Problem 23

Problem

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

$\text{(A)} \ \frac{4}{3} \qquad \text{(B)} \ \frac{3}{2} \qquad \text{(C)} \ \frac{3\sqrt{5}}{5} \qquad \text{(D)}\ \frac{2\sqrt{5}}{3}\qquad \text{(E)}\ \text{not uniquely determined}$

Solution

$\fbox{}$

1980 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 22	Followed by Problem 24
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1980 AHSME Problems/Problem 23

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