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Answer: Approximately 4.47 km</h3>
The exact answer is 2*sqrt(5) but I figured it makes more sense to represent distance in terms of the approximate value. Round that however you need to. Your teacher may or may not want you to include the units, so be sure to ask.
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Explanation:
This is similar to the previous question I answered earlier. Draw a vertical line straight down from point X until you reach line YZ. Mark point W on this vertical line, and that's also on line YZ.
Point W is the midpoint of YZ, which cuts it in half.
Let's focus on triangle WXY. It's horizontal leg is 8/2 = 4 km. Let a = 4.
For that same triangle, the vertical leg is unknown. We'll call it h. So b = h.
The hypotenuse of this right triangle is YX = 6 km. Let c = 6.
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We have
Use the pythagorean theorem from here
a^2 + b^2 = c^2
4^2 + h^2 = 6^2
16 + h^2 = 36
h^2 = 36-16
h^2 = 20
h = sqrt(20)
h = sqrt(4*5)
h = sqrt(4)*sqrt(5)
h = 2*sqrt(5) ..... exact
h = 4.47213595 ..... approximate
h = 4.47 km
The distance is roughly 4.47 km
