Question

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

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 24\), \(c = 25\), and we need to find \(b\). Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 24\) and \(c = 25\) into the formula: \(b^{2}=25^{2}-24^{2}\).
Since \(25^{2}=625\) and \(24^{2}=576\), then \(b^{2}=625 - 576=49\).

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{49}\).

Answer:

\(7\)