1980 AHSME Problems/Problem 9

Problem

A man walks $x$ miles due west, turns $150^\circ$ to his left and walks 3 miles in the new direction. If he finishes a a point $\sqrt{3}$ from his starting point, then $x$ is

$\text{(A)} \ \sqrt 3 \qquad \text{(B)} \ 2\sqrt{5} \qquad \text{(C)} \ \frac 32 \qquad \text{(D)} \ 3 \qquad \text{(E)} \ \text{not uniquely determined}$

Solution

Let us think about this. We only know that he ends up $\sqrt{3}$ away from the origin. However, think about the locus of points $\sqrt{3}$ away from the origin, a circle. However, his path could end on any part of the circle below the $x-$ axis, so therefore, the answer is $\fbox{E: not uniquely determined}.$

(Note: Another way to do this is using law of cosines, which yields two solutions for x.)

1980 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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1980 AHSME Problems/Problem 9

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