Question

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

Explanation:

Step1: Identify triangle type

It's a right triangle (has right angle symbol), so use Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse (longest side, 26 here), \(a = 24\), \(b\) is unknown.

Step2: Rearrange formula for \(b\)

\(b = \sqrt{c^2 - a^2}\)

Step3: Substitute values

\(c = 26\), \(a = 24\), so \(b = \sqrt{26^2 - 24^2}\)

Step4: Calculate squares

\(26^2 = 676\), \(24^2 = 576\)

Step5: Subtract and take square root

\(b = \sqrt{676 - 576} = \sqrt{100} = 10\)

Answer:

10