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 can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 10\) and \(b = 24\), and we need to find the hypotenuse \(c\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 10\) and \(b = 24\) into the formula \(c=\sqrt{a^{2}+b^{2}}\). First, calculate \(a^{2}\) and \(b^{2}\): \(a^{2}=10^{2}=100\) and \(b^{2}=24^{2} = 576\). Then, \(a^{2}+b^{2}=100 + 576=676\).

Step3: Find the square root

Now, find the square root of 676. Since \(\sqrt{676}=26\) (because \(26\times26 = 676\)).

Answer:

26