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 \(c = 16\), \(b=12\), and \(a = x\). So \(x^{2}+12^{2}=16^{2}\).

Step2: Simplify the equation

\(x^{2}=16^{2}-12^{2}\). Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(16 + 12)(16-12)=(28)\times(4)=112\).

Step3: Solve for \(x\)

\(x=\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\approx4\times2.6458\approx10.58\)

Answer:

\(x\approx10.58\)