Question

find the length of the third side. if necessary, round to the nearest tenth.
7
6

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 legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 7\) and \(b = 6\), and we need to find the hypotenuse \(c\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 7\) and \(b = 6\) into the formula \(c=\sqrt{a^{2}+b^{2}}\). So \(c=\sqrt{7^{2}+6^{2}}=\sqrt{49 + 36}=\sqrt{85}\).

Step3: Calculate the value and round

\(\sqrt{85}\approx9.2\) (rounded to the nearest tenth).

Answer:

The length of the third side is approximately \(9.2\).