Question

use your notes in your packet to show work.
set up the problem
solution: x = in (rounded to the nearest hundredths)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 3\) and \(b = 12\) and hypotenuse \(c=x\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So, \(3^{2}+12^{2}=x^{2}\).

Step2: Calculate \(3^{2}+12^{2}\)

\(3^{2}=9\) and \(12^{2}=144\). Then \(3^{2}+12^{2}=9 + 144=153\). So, \(x^{2}=153\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{153}\). Using a calculator, \(\sqrt{153}\approx12.37\).

Answer:

Set up the problem: \(3^{2}+12^{2}=x^{2}\)
Solution: \(x = 12.37\) in.