Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Let \(c = 25\), \(a=16\), and we want to find \(b\). Then \(b^{2}=c^{2}-a^{2}\).
Substitute \(c = 25\) and \(a = 16\) into the formula: \(b^{2}=25^{2}-16^{2}\).
Calculate \(25^{2}=625\) and \(16^{2}=256\). So \(b^{2}=625 - 256\).

Step2: Calculate \(b^{2}\)

\(b^{2}=625-256=369\).

Step3: Find \(b\)

\(b=\sqrt{369}\). Since \(\sqrt{369}\approx19.2\) (using a calculator, \(\sqrt{369}=\sqrt{9\times41}=3\sqrt{41}\approx3\times6.403 = 19.209\approx19.2\)).

Answer:

\(19.2\)