Question

find the length of the third side. if necessary, round to the nearest tenth.

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, \(c = 25\), \(a = 7\), and we need to find \(b\).

Step2: Rearrange the formula

To find \(b\), we rearrange the Pythagorean theorem: \(b = \sqrt{c^2 - a^2}\)

Step3: Substitute the values

Substitute \(c = 25\) and \(a = 7\) into the formula: \(b = \sqrt{25^2 - 7^2}\)

Step4: Calculate the squares

Calculate \(25^2 = 625\) and \(7^2 = 49\), so \(b = \sqrt{625 - 49}\)

Step5: Subtract inside the square root

\(625 - 49 = 576\), so \(b = \sqrt{576}\)

Step6: Find the square root

\(\sqrt{576} = 24\)

Answer:

24