Question

solve for x to the nearest tenth. 8 7 x 6 answer attempt 2 out of 3 x ≈ submit answer

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\). First, find the length of the common hypotenuse of the two right - triangles. For the triangle with legs \(7\) and \(8\), let the hypotenuse be \(h\). Then \(h^{2}=7^{2}+8^{2}=49 + 64=113\).

Step2: Use the Pythagorean theorem again

For the right - triangle with legs \(6\) and \(h\) (where \(h^{2}=113\)) and hypotenuse \(x\), by the Pythagorean theorem \(x^{2}=h^{2}+6^{2}\). Substitute \(h^{2}=113\) into the equation: \(x^{2}=113+36=149\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{149}\approx12.2\).

Answer:

\(12.2\)