Question

summerfield is 7 miles due north of the airport, and cedarburg is due east of the airport. if the distance between summerfield and cedarburg is 9 miles, how far is cedarburg from the airport? if necessary, round to the nearest tenth. miles submit

Explanation:

Step1: Apply Pythagorean theorem

Let the distance from the airport to Cedarburg be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 7\), \(c=9\), and \(b=x\). So \(7^{2}+x^{2}=9^{2}\).

Step2: Simplify the equation

\(49+x^{2}=81\). Then \(x^{2}=81 - 49\).

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

\(x^{2}=32\).

Step4: Solve for \(x\)

\(x=\sqrt{32}\approx5.7\)

Answer:

\(5.7\)