Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(a\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 7\) (hypotenuse) and \(b = 3\) (one of the legs). So \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute values

Substitute \(c = 7\) and \(b = 3\) into the formula: \(a^{2}=7^{2}-3^{2}=49 - 9=40\).

Step3: Solve for \(a\)

Take the square root of both sides: \(a=\sqrt{40}\approx6.3\).

Answer:

\(6.3\)