Answer:
a^2 + b^2 = c^2 (pythagorean theorem)
a^2 + 40^2 = 41^2 (plug in the known values)
a^2 + 1,600 = 1681 (simplify what you can)
a^2 = 81 (subtracted 1600 from both sides)
a= (81 under a radical) (I think this is what your answer will be, based on the problem)
a=9 (what the fully simplified answer is)