Answer:
4×sqrt(5) inches
Explanation:
Pythagorean theorem states that (for right triangles) if you square each shorter side and add those together, you will get the sum of the longest side (hypotenuse) squared.
This is commonly written as:
a^2 + b^2 = c^2, where c is the hypotenuse.
((For right triangles this will always be opposite the 90° angle.))
Since you know one of the shorter sides and the hypotenuse, rewrite the equation as such:
c^2 - b^2 = a^2, where a is the unknown length
This goes to:
sqrt(c^2 - b^2) = a
sqrt((12in)^2 - (8in)^2) = a
sqrt(144sqin - 64sqin) = sqrt(80sqin) = a
This simplifies to:
sqrt(16sqin)×sqrt(5sqin) = 4in×sqrt(5sqin) = a