Question

question
find the length of the third side. if necessary, round to the nearest tenth.
answer
attempt 2 out of 8
21.8

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 10\) and \(b = 24\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
Substitute \(a = 10\) and \(b = 24\) into the formula: \(10^{2}+24^{2}=c^{2}\).
Calculate \(10^{2}=100\) and \(24^{2}=576\). Then \(100 + 576=c^{2}\), so \(c^{2}=676\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{676}\).
Since \(\sqrt{676}=26\).

Answer:

\(26\)