Difference between revisions of "1980 AHSME Problems/Problem 9"

m (Solution)
(Solution)
 
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Let us think about this. We only know that he ends up <math>\sqrt{3}</math> away from the origin. However, think about the locus of points <math>\sqrt{3}</math> away from the origin, a circle. However, his path could end on any part of the circle below the <math>x-</math>axis, so therefore, the answer is
 
Let us think about this. We only know that he ends up <math>\sqrt{3}</math> away from the origin. However, think about the locus of points <math>\sqrt{3}</math> away from the origin, a circle. However, his path could end on any part of the circle below the <math>x-</math>axis, so therefore, the answer is
 
<math>\fbox{E: not uniquely determined}.</math>
 
<math>\fbox{E: not uniquely determined}.</math>
 +
 +
(Note: Another way to do this is using law of cosines, which yields two solutions for x.)
  
 
== See also ==
 
== See also ==

Latest revision as of 16:00, 20 March 2018

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.)

See also

1980 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

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