Answer
a=9
Work Step by Step
Use the Pythagorean Theorem to find the missing length.
$a^2+b^2=c^2\longrightarrow$ substitute the given values
$a^2+40^2=41^2\longrightarrow$ simplify exponents
$a^2+1600=1681\longrightarrow$ subtract 1600 from each side
$a^2+1600-1600=1681-1600\longrightarrow$ subtract
$a^2=81\longrightarrow$ find the square root of each side
$\sqrt{a^2}=\sqrt{81}\longrightarrow$ simplify
$a=9$
