Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 7\), \(b = 8\), and \(c\) is the hypotenuse.
$$c^{2}=7^{2}+8^{2}$$

Step2: Calculate \(7^{2}\) and \(8^{2}\)

\(7^{2}=49\), \(8^{2}=64\). Then \(c^{2}=49 + 64\).
$$c^{2}=113$$

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{113}\).
$$c\approx10.6$$

Answer:

\(10.6\)