Difference between revisions of "2003 AMC 8 Problems/Problem 20"
(→Solution) |
(→Solution) |
||
Line 9: | Line 9: | ||
Imagine the clock as a circle. The minute hand will be at the 4 at 20 minutes past the hour. The central angle formed between <math>4</math> and <math>5</math> is <math>30</math> degrees (since it is 1/12 of a full circle, 360). By <math>4:20</math>, the hour hand would have moved <math>\frac{1}{3}</math> way from 4 to 5 since <math>\frac{20}{60}</math> is reducible to <math>\frac{1}{3}</math>. One third of the way from 4 to 5 is one third of 30 degrees, which is 10 degrees past the 4. Recall that the minute hand is at the 4, so the angle between them is <math>\boxed{10, D}</math>, and we are done. | Imagine the clock as a circle. The minute hand will be at the 4 at 20 minutes past the hour. The central angle formed between <math>4</math> and <math>5</math> is <math>30</math> degrees (since it is 1/12 of a full circle, 360). By <math>4:20</math>, the hour hand would have moved <math>\frac{1}{3}</math> way from 4 to 5 since <math>\frac{20}{60}</math> is reducible to <math>\frac{1}{3}</math>. One third of the way from 4 to 5 is one third of 30 degrees, which is 10 degrees past the 4. Recall that the minute hand is at the 4, so the angle between them is <math>\boxed{10, D}</math>, and we are done. | ||
− | Solution 2 | + | ==Solution 2== |
You may also use the formula <math>30h-5.5m</math> to yield a result in only ~10 seconds | You may also use the formula <math>30h-5.5m</math> to yield a result in only ~10 seconds |
Revision as of 19:44, 12 December 2019
Contents
[hide]Problem
What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?
Solution
Imagine the clock as a circle. The minute hand will be at the 4 at 20 minutes past the hour. The central angle formed between and is degrees (since it is 1/12 of a full circle, 360). By , the hour hand would have moved way from 4 to 5 since is reducible to . One third of the way from 4 to 5 is one third of 30 degrees, which is 10 degrees past the 4. Recall that the minute hand is at the 4, so the angle between them is , and we are done.
Solution 2
You may also use the formula to yield a result in only ~10 seconds
-sub_math
See Also
2003 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.