Question

if an airplane passes directly over your head at an altitude of 9 kilometers, how far is the airplane from your position after it has flown 12 kilometers farther at the same altitude?

Explanation:

Step1: Recognize right - triangle

The vertical distance from you to the airplane (altitude) is one leg of a right - triangle ($a = 9$ km), and the horizontal distance the airplane has flown is the other leg ($b = 12$ km). We want to find the hypotenuse $c$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. Substitute $a = 9$ and $b = 12$ into the formula: $c^{2}=9^{2}+12^{2}=81 + 144=225$.

Step3: Solve for $c$

Take the square root of both sides. Since $c>0$, $c=\sqrt{225}=15$.

Answer:

15