Question

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

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side of a right - triangle). Here, \(c = 26\) and one side \(a = 24\).

Step2: Rearrange the formula

We want to find the other side \(b\). Rearranging the Pythagorean theorem gives \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute values

Substitute \(c = 26\) and \(a = 24\) into the formula: \(b=\sqrt{26^{2}-24^{2}}=\sqrt{(26 + 24)(26 - 24)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)).

Step4: Calculate

First, \((26 + 24)(26 - 24)=(50)\times(2)=100\). Then, \(b=\sqrt{100}=10\).

Answer:

10