Question

for the following right - triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, if the two legs are \(a\) and \(b\) and the hypotenuse is \(c\), then \(a^{2}+b^{2}=c^{2}\). Here, let \(a = x\), \(b = 12\), and \(c = 16\). So \(x^{2}+12^{2}=16^{2}\).

Step2: Simplify the equation

\(x^{2}+144 = 256\). Then \(x^{2}=256 - 144\).

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

\(x^{2}=112\).

Step4: Solve for \(x\)

\(x=\sqrt{112}\approx10.58\).

Answer:

\(10.58\)