Question

find the length of the leg x, as an exact value or to at least 2 decimal places.
x =

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 16\), \(b=6\), and \(a = x\). So \(x^{2}+6^{2}=16^{2}\).

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

\(x^{2}=16^{2}-6^{2}\). Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(16 + 6)(16-6)=22\times10 = 220\).

Step3: Find \(x\)

\(x=\sqrt{220}\approx14.83\)

Answer:

\(14.83\)