Question

flight an airplane lands at an airport 60 miles east and 25 miles north of where it took off.
the two airports are \boxed{} miles apart.

Explanation:

Step1: Identify the triangle type

The problem involves a right - triangle, where the two legs are 60 miles (east - west direction) and 25 miles (north - south direction). We can use the Pythagorean theorem, which states that for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 60\) and \(b=25\).

Step2: Calculate \(a^{2}+b^{2}\)

First, calculate \(a^{2}\) and \(b^{2}\). \(a^{2}=60^{2}=60\times60 = 3600\) and \(b^{2}=25^{2}=25\times25 = 625\). Then, \(a^{2}+b^{2}=3600 + 625=4225\).

Step3: Calculate the hypotenuse \(c\)

Now, find the square root of \(4225\). Since \(\sqrt{4225}=65\) (because \(65\times65 = 4225\)).

Answer:

65