2020 AMC 10B Problems/Problem 4
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
Solution 2
Looking at the answer choices, only and
are coprime to
. Testing
makes the other angle
which is prime, therefore our answer is
Video Solution
~IceMatrix
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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