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 \(a = 6\) and \(b\), and hypotenuse \(c=7\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). We need to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 6\) and \(c = 7\) into the formula: \(b=\sqrt{7^{2}-6^{2}}=\sqrt{49 - 36}=\sqrt{13}\).

Step3: Calculate the value

\(\sqrt{13}\approx3.6\) (rounded to the nearest tenth).

Answer:

\(3.6\)