Questions: Find the length of the third side. If necessary, write in simplest radical form.

Solution Steps

We are given a right triangle with two sides given: a leg of length 3 and a hypotenuse of length 5.

Let the length of the third side be \(x\). The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So, we have \(3^2 + x^2 = 5^2\).

Simplifying the equation, we have \(9 + x^2 = 25\). Subtracting 9 from both sides, we get \(x^2 = 16\). Taking the square root of both sides, we find \(x = \sqrt{16} = 4\).

Final Answer