Question

what is the length of the missing leg? if necessary, round to the nearest tenth. b = millimeters

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 \(c = 17\) mm and \(a = 8\) mm. 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 \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(17^{2}=289\) and \(8^{2}=64\), then \(b=\sqrt{289 - 64}=\sqrt{225}\).

Step3: Calculate the square - root

\(\sqrt{225}=15\)

Answer:

15