The word 'rational' in 'rational numbers' comes from the word 'ratio.' That is because rational numbers are those numbers which can be obtained when one integer is divided by another integer. For example, the number 8 is a rational number because it results when the integer 24 is divided by the integer 3, as in the ratio 24/3.
If the upper triangle has a right angle at Island C, we need only use the Pythagorean Theorem to find x:
(10 mi)^2 + (20 mi)^2 = x^2, so that
x^2 = 100 mi^2 + 400 mi^2 = 500 mi^2, which reduces to
x = +10√5 mi
Note that the shortest side (10 mi) is adjacent to a 30 degree angle. Thus, the upper triangle is a 30-60-90 triangle, meaning that the Pythagorean Theorem DOES apply here.
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