Difference between revisions of "1999 AMC 8 Problems/Problem 2"
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− | <math>\ | + | <math>\textbf{(A)}\ 30 \qquad \textbf{(B)}\ 45 \qquad \textbf{(C)}\ 60 \qquad \textbf{(D)}\ 75 \qquad \textbf{(E)}\ 90</math> |
==Solution 1== | ==Solution 1== | ||
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At <math>10:00</math>, the hour hand will be on the <math>10</math> while the minute hand on the <math>12</math>. | At <math>10:00</math>, the hour hand will be on the <math>10</math> while the minute hand on the <math>12</math>. | ||
− | This makes them <math>\frac{1}{6}</math>th of a circle apart, and <math>\frac{1}{6}\cdot360^{\circ}=\boxed{ | + | This makes them <math>\frac{1}{6}</math>th of a circle apart, and <math>\frac{1}{6}\cdot360^{\circ}=\boxed{\textbf{(C) } 60}</math>. |
==Solution 2== | ==Solution 2== | ||
We know that the full clock is a circle, and therefore has 360 degrees. Considering that there are <math>12</math> numbers, the distance between one number will be <math>360\div 12=30</math>. | We know that the full clock is a circle, and therefore has 360 degrees. Considering that there are <math>12</math> numbers, the distance between one number will be <math>360\div 12=30</math>. | ||
− | If the time is <math>10:00</math>, then the hour hand will be on <math>10</math>, and the minute hand will be on, <math>12</math>, making them <math>2</math> numbers apart, so they will be <math>60</math> degrees apart, or <math>\boxed{ | + | If the time is <math>10:00</math>, then the hour hand will be on <math>10</math>, and the minute hand will be on, <math>12</math>, making them <math>2</math> numbers apart, so they will be <math>60</math> degrees apart, or <math>\boxed{\textbf{(C) } 60}</math> |
==See Also== | ==See Also== |
Latest revision as of 21:45, 15 January 2024
Contents
Problem
What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?
Solution 1
At , the hour hand will be on the
while the minute hand on the
.
This makes them th of a circle apart, and
.
Solution 2
We know that the full clock is a circle, and therefore has 360 degrees. Considering that there are numbers, the distance between one number will be
.
If the time is
, then the hour hand will be on
, and the minute hand will be on,
, making them
numbers apart, so they will be
degrees apart, or
See Also
1999 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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.