Question

what is the value of $x$? round to the nearest tenth, if necessary

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(c = 15\), \(b=7\), and \(a = x\). So \(x^{2}+7^{2}=15^{2}\).

Step2: Simplify the equation

\(x^{2}+49 = 225\). Then \(x^{2}=225 - 49\).

Step3: Calculate \(x^{2}\)

\(x^{2}=176\).

Step4: Solve for \(x\)

\(x=\sqrt{176}\approx13.3\)

Answer:

\(x\approx13.3\)