Question 1182670: A pitcher throws a baseball 60 feet from the pitcher's mound to home plate. A batter pops the ball up and it comes down just 24 feet from home plate. What can you determine about how far the ball lands from pitcher's mound? Describe the shortest and longest possible distances. Triangle Inequality Theorem.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
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.
Two sides of the triangle have lengths 60 and 24.
(1) If 60 is the longest side, then the third side x must be such that
24+x>=60
x>=36
(2) if the third side x is the longest, then
60+24>=x
x<=84
ANSWER: the least possible distance from the pitcher's mound is 36 feet; the greatest is 84 feet.
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.
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