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Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 28 kilometers28\,\text{kilometers}, and the eastbound airplane has traveled 96 kilometers96\,\text{kilometers}. How far apart are the two airplanes?\newline_____\_\_\_\_\_ kilometers

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Full solution

Q. Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 28 kilometers28\,\text{kilometers}, and the eastbound airplane has traveled 96 kilometers96\,\text{kilometers}. How far apart are the two airplanes?\newline_____\_\_\_\_\_ kilometers
  1. Identify Triangle: Identify the right triangle formed by the paths of the airplanes.\newlineNorthbound distance: 28 km28\,\text{km}\newlineEastbound distance: 96 km96\,\text{km}\newlineDistance apart (hypotenuse): xx
  2. Use Pythagorean Theorem: Use the Pythagorean Theorem to find the distance apart. a2+b2=c2a^2 + b^2 = c^2 282+962=x228^2 + 96^2 = x^2
  3. Calculate Leg Squares: Calculate the squares of the legs.\newline282=78428^2 = 784\newline962=921696^2 = 9216
  4. Add Squares for Hypotenuse: Add the squares of the legs to find the square of the hypotenuse.\newline784+9216=x2784 + 9216 = x^2\newline10000=x210000 = x^2
  5. Take Square Root: Take the square root of both sides to solve for xx.10000=x2\sqrt{10000} = \sqrt{x^2}x=100x = 100

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