Question 1182670
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Note for this application of the triangle inequality, a degenerate triangle is possible -- that is, the sum of the lengths of the two shorter sides can be equal to the longest side; the sum does not have to be greater than the longest side.<br>
Two sides of the triangle have lengths 60 and 24.<br>
(1) If 60 is the longest side, then the third side x must be such that<br>
24+x>=60
x>=36<br>
(2) if the third side x is the longest, then
60+24>=x
x<=84<br>
ANSWER: the least possible distance from the pitcher's mound is 36 feet; the greatest is 84 feet.<br>
Obviously the least possible distance is if the popup was directly toward the pitcher's mound from home plate; the greatest is if the popup was directly behind home plate from the pitcher's mound.<br>