Question

find the length of the third side. if necessary, round to the nearest tenth.
16
12

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). In this triangle, the hypotenuse is \(16\), one leg is \(12\), and we need to find the other leg (let's call it \(x\)). So the formula becomes \(16^{2}=x^{2}+12^{2}\).

Step2: Rearrange the formula to solve for \(x\)

We can rewrite the formula as \(x^{2}=16^{2}-12^{2}\). Calculate \(16^{2}=256\) and \(12^{2} = 144\). Then \(x^{2}=256 - 144=112\).

Step3: Find the value of \(x\)

Take the square root of both sides: \(x=\sqrt{112}\). Simplify \(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\approx4\times2.6458\approx10.6\) (rounded to the nearest tenth).

Answer:

\(10.6\)