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 $b=90^{\circ]-89^{\circ}=1^{\circ}$ (Error compiling LaTeX. Unknown error_msg), which is not prime.
The next greatest prime number less than is
. If
, then
, which IS prime, so we have our answer
~quacker88