Question

find the value of x to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let's consider the right - triangle formed. The hypotenuse of the right - triangle is 8 and one of the legs is 4. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. Let \(x\) be the other leg, then \(x^{2}+4^{2}=8^{2}\).

Step2: Solve for \(x^{2}\)

We can rewrite the equation as \(x^{2}=8^{2}-4^{2}\). Calculate \(8^{2}=64\) and \(4^{2}=16\). So \(x^{2}=64 - 16=48\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{48}\approx6.9\) (rounded to the nearest tenth).

Answer:

\(6.9\)