Question 1163386
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The center of each crossbar is 3 feet from each goalpost (half the length of the crossbar).<br>
Imagine a third post midway between the two goal posts.  It of course will have the same height as the two goalposts.<br>
That center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.  By the Pythagorean Theorem, the other leg -- the height of each post -- is 4 feet.<br>