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, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 19\), \(b = 12\), and \(a=x\). So, \(x^{2}+12^{2}=19^{2}\).

Step2: Simplify the equation

\(x^{2}+144 = 361\). Then, \(x^{2}=361 - 144\).

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

\(x^{2}=217\).

Step4: Solve for \(x\)

\(x=\sqrt{217}\approx14.73\)

Answer:

\(14.73\)