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, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(a = x\), \(b = 3\), \(c=7.6\). So the equation is \(x^{2}+3^{2}=7.6^{2}\).

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

\(x^{2}=7.6^{2}-3^{2}\).
Calculate \(7.6^{2}=7.6\times7.6 = 57.76\) and \(3^{2}=9\). Then \(x^{2}=57.76 - 9=48.76\).

Step3: Solve for \(x\)

\(x=\sqrt{48.76}\approx6.98\) (rounded to the nearest hundredths).

Answer:

Set up the problem: \(x^{2}+3^{2}=7.6^{2}\)
Solution: \(x = 6.98\) in.