Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 28 kilometers, and the eastbound airplane has traveled 96 kilometers. How far apart are the two airplanes? _____ kilometers

Identify Triangle: Identify the right triangle formed by the paths of the airplanes. Northbound distance: 28 km Eastbound distance: 96 km Distance apart (hypotenuse): xUse Pythagorean Theorem: Use the Pythagorean Theorem to find the distance apart. a^2 + b^2 = c^2 28^2 + 96^2 = x^2Calculate Leg Squares: Calculate the squares of the legs. 28^2 = 784 96^2 = 9216Add Squares for Hypotenuse: Add the squares of the legs to find the square of the hypotenuse. 784 + 9216 = x^2 10000 = x^2Take Square Root: Take the square root of both sides to solve for x. sqrt(10000) = sqrt(x^2) x = 100

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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 $28\,\text{kilometers}$ , and the eastbound airplane has traveled $96\,\text{kilometers}$ . How far apart are the two airplanes? $\newline$ $\_\_\_\_\_$ kilometers

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Pythagorean Theorem and its converse

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Q. Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled

28\,\text{kilometers}

, and the eastbound airplane has traveled

96\,\text{kilometers}

. How far apart are the two airplanes?

\newline

\_\_\_\_\_

kilometers

Identify Triangle: Identify the right triangle formed by the paths of the airplanes. $\newline$ Northbound distance: $28\,\text{km}$ $\newline$ Eastbound distance: $96\,\text{km}$ $\newline$ Distance apart (hypotenuse): $x$
Use Pythagorean Theorem: Use the Pythagorean Theorem to find the distance apart. $a^2 + b^2 = c^2$ $28^2 + 96^2 = x^2$
Calculate Leg Squares: Calculate the squares of the legs. $\newline$ $28^2 = 784$ $\newline$ $96^2 = 9216$
Add Squares for Hypotenuse: Add the squares of the legs to find the square of the hypotenuse. $\newline$ $784 + 9216 = x^2$ $\newline$ $10000 = x^2$
Take Square Root: Take the square root of both sides to solve for $x$ . $\sqrt{10000} = \sqrt{x^2}$ $x = 100$