Difference between revisions of "1980 AHSME Problems/Problem 9"
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<math>\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}</math> | <math>\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}</math> | ||
| + | |||
| + | == Solution == | ||
| + | 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> | ||
| + | |||
| + | (Note: Another way to do this is using law of cosines, which yields two solutions for x.) | ||
| + | |||
| + | == See also == | ||
| + | {{AHSME box|year=1980|num-b=8|num-a=10}} | ||
| + | |||
| + | [[Category: Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 15:00, 20 March 2018
Problem
A man walks 
miles due west, turns 
to his left and walks 3 miles in the new direction. If he finishes a a point 
from his starting point, then is
Solution
Let us think about this. We only know that he ends up away from the origin. However, think about the locus of points away from the origin, a circle. However, his path could end on any part of the circle below the 
axis, so therefore, the answer is
(Note: Another way to do this is using law of cosines, which yields two solutions for x.)
See also
| 1980 AHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
