Question

solve for x to the nearest tenth.

Explanation:

Step1: Find the length of the common hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for the first right - triangle (with legs \(4\) and \(8\)).
\(c=\sqrt{4^{2}+8^{2}}=\sqrt{16 + 64}=\sqrt{80}\)

Step2: Solve for \(x\) using the Pythagorean theorem again

For the second right - triangle (with legs \(7\) and \(x\) and hypotenuse \(\sqrt{80}\)).
\(x=\sqrt{(\sqrt{80})^{2}-7^{2}}=\sqrt{80 - 49}=\sqrt{31}\approx5.6\)

Answer:

\(5.6\)