Question

question find the length of the third side. if necessary, round to the nearest tenth.
answer attempt 1 out of 2

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the unknown side be \(a\), \(b = 24\), \(c=26\). Then \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute values

\(a^{2}=26^{2}-24^{2}\).
Since \(26^{2}=(20 + 6)^{2}=400+240 + 36=676\) and \(24^{2}=(20+4)^{2}=400 + 160+16 = 576\).
So \(a^{2}=676-576\).

Step3: Calculate \(a^{2}\) and \(a\)

\(a^{2}=100\), then \(a=\sqrt{100}=10\).

Answer:

\(10\)