find the length of the third side. if necessary, round to the nearest tenth.

Answer

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem (a^{2}+b^{2}=c^{2}) for a right - triangle, where (c) is the hypotenuse. Here, (c = 17) and (a = 8), and we need to find (b).

Step2: Rearrange the formula

We get (b=\sqrt{c^{2}-a^{2}}).

Step3: Substitute values

Substitute (c = 17) and (a = 8) into the formula: (b=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}) (using (x^{2}-y^{2}=(x + y)(x - y))). First, (17+8 = 25) and (17 - 8=9), so (b=\sqrt{25\times9}=\sqrt{225}).

Step4: Calculate the result

(b = 15).