Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 16\) and \(b = 45\), and hypotenuse \(c\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 16\) and \(b = 45\) into the formula: \(c=\sqrt{16^{2}+45^{2}}\).
First, calculate \(16^{2}=256\) and \(45^{2}=2025\). Then \(16^{2}+45^{2}=256 + 2025=2281\).
So \(c=\sqrt{2281}\).

Step2: Calculate the square root

\(\sqrt{2281}\approx47.8\)

Answer:

\(47.8\)