Question

find the length of the third side. if necessary, write in simplest radical form. 5 \sqrt{34} answer attempt 1 out of 3

Explanation:

Step1: Identify the triangle type

This is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a, b\) are the legs. Here, one leg \(a = 5\), hypotenuse \(c=\sqrt{34}\), and we need to find the other leg \(b\).

Step2: Rearrange the Pythagorean theorem

We solve for \(b\): \(b^2 = c^2 - a^2\)

Step3: Substitute the values

Substitute \(a = 5\) and \(c=\sqrt{34}\) into the formula: \(b^2 = (\sqrt{34})^2 - 5^2\)

Step4: Calculate the values

\((\sqrt{34})^2 = 34\) and \(5^2 = 25\), so \(b^2 = 34 - 25 = 9\)

Step5: Find \(b\)

Take the square root of both sides: \(b=\sqrt{9}=3\)

Answer:

3