If the length of one leg of a right triangle is 3 and the hypotenuse is [tex]\sqrt{34}[/tex], what is the length of the other leg?

[tex]\huge{\boxed{5}}[/tex]The Pythagorean theorum states that when [tex]a[/tex] and [tex]b[/tex] are sides and [tex]c[/tex] is the hypotenuse, [tex]a^2 + b^2 = c^2[/tex]So, let's plug in the values. [tex]3^2 + b^2 = (\sqrt{34})^2[/tex]Simplify. The square of a square root is the number inside the square root. [tex]9 + b^2 = 34[/tex]Subtract 9 from both sides. [tex]b^2 = 25[/tex]Get the square root of both sides. [tex]\sqrt{b^2} = \sqrt{25}[/tex][tex]b=\boxed{5}[/tex]