Question

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Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here \(c = 17\mathrm{cm}\), \(a = 8\mathrm{cm}\), and we want to find \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 17\) and \(a = 8\) into the formula: \(b=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{25\times9}=\sqrt{225}\).

Step3: Calculate the square - root

\(\sqrt{225}=15\).

Answer:

\(15\mathrm{cm}\)