Difference between revisions of "2020 AMC 10B Problems/Problem 4"
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The next greatest prime number less than <math>90</math> is <math>83</math>. If <math>a=83^{\circ}</math>, then <math>b=7^{\circ}</math>, which IS prime, so we have our answer <math>\boxed{\textbf{(D)}\ 7}</math> ~quacker88 | The next greatest prime number less than <math>90</math> is <math>83</math>. If <math>a=83^{\circ}</math>, then <math>b=7^{\circ}</math>, which IS prime, so we have our answer <math>\boxed{\textbf{(D)}\ 7}</math> ~quacker88 | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/Gkm5rU5MlOU | ||
| + | |||
| + | ~IceMatrix | ||
==See Also== | ==See Also== | ||
Revision as of 17:28, 7 February 2020
Contents
Problem
The acute angles of a right triangle are 
and 
, where 
and both 
and 
are prime numbers. What is the least possible value of ?
Solution
Since the three angles of a triangle add up to 
and one of the angles is 
because it's a right triangle, then 
.
The greatest prime number less than 
is 
. If 
, then 
, which is not prime.
The next greatest prime number less than is 
. If 
, then 
, which IS prime, so we have our answer 
~quacker88
Video Solution
~IceMatrix
See Also
| 2020 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
