Question

a student pilot filed a flight plan which included flying due west from an airport in dallas, texas for 100 miles, then turning due north and flying 75 miles to land at an airport in wichita falls, texas. how far would he then have to fly in a straight line distance to get back to dallas? 200 miles 175 miles 25 miles 125 miles

Explanation:

Step1: Apply Pythagorean theorem

The path forms a right - triangle. Let \(a = 100\) miles (west - east side) and \(b=75\) miles (north - south side). The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse (straight - line distance).
So, \(c^{2}=100^{2}+75^{2}\).

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

\(100^{2}=10000\) and \(75^{2}=5625\). Then \(c^{2}=10000 + 5625=15625\).

Step3: Find \(c\)

Take the square root of \(c^{2}\). \(c=\sqrt{15625}\). Since \(125\times125 = 15625\), \(c = 125\).

Answer:

125 miles