Question

find the length of the third side. if necessary, round to the nearest tenth.
24
10
answer attempt 1 out of 8
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 10\), \(b\) (unknown) and hypotenuse \(c = 24\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). We need to solve for \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 10\) and \(c = 24\) into the formula: \(b=\sqrt{24^{2}-10^{2}}=\sqrt{576 - 100}=\sqrt{476}\).

Step3: Calculate the square - root

\(\sqrt{476}\approx21.8\) (rounded to the nearest tenth).

Answer:

\(21.8\)