Difference between revisions of "2003 AMC 12B Problems/Problem 21"
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An object moves <math>8</math> cm in a straight [[line]] from <math>A</math> to <math>B</math>, turns at an angle <math>\alpha</math>, measured in radians and chosen at random from the interval <math>(0,\pi)</math>, and moves <math>5</math> cm in a straight line to <math>C</math>. What is the [[probability]] that <math>AC < 7</math>? | An object moves <math>8</math> cm in a straight [[line]] from <math>A</math> to <math>B</math>, turns at an angle <math>\alpha</math>, measured in radians and chosen at random from the interval <math>(0,\pi)</math>, and moves <math>5</math> cm in a straight line to <math>C</math>. What is the [[probability]] that <math>AC < 7</math>? | ||
− | <math>\mathrm{(A)}\ | + | <math>\mathrm{(A)}\ \frac{1}{6} |
− | \qquad\mathrm{(B)}\ | + | \qquad\mathrm{(B)}\ \frac{1}{5} |
− | \qquad\mathrm{(C)}\ | + | \qquad\mathrm{(C)}\ \frac{1}{4} |
− | \qquad\mathrm{(D)}\ | + | \qquad\mathrm{(D)}\ \frac{1}{3} |
− | \qquad\mathrm{(E)}\ | + | \qquad\mathrm{(E)}\ \frac{1}{2}</math> |
== Solution == | == Solution == |
Revision as of 13:15, 29 November 2008
Problem
An object moves cm in a straight line from
to
, turns at an angle
, measured in radians and chosen at random from the interval
, and moves
cm in a straight line to
. What is the probability that
?
Solution
By the Law of Cosines,
It follows that , and the probability is
.
See also
2003 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
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 | |
All AMC 12 Problems and Solutions |