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Expert: - 4/5/2009


Question
A 200 foot tower on the side of a hill that form a 5 degree angle with the horizontal.  Find the length of the two guy wire that are anchored 150 feet uphill and downhill from the tower's base and extend to the top of the tower. Round to the nearest tenth of a foot.


A Little League baseball diamond has four bases forming a square whose sides measure 90 feet each.  The pitcher's mound is 60.5 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher's mound to first base.  Round to the nearest tenth of a foot.




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Answer
A Little League baseball diamond has four bases forming a square whose sides between the bases measure 90 feet each .  The pitcher's mound is 60.5 feet from home plate on a line joining home plate and second base.

I will assume all measurements are from the center of each base and the pitchers mound.  THe answers I give will assume that as well.

Note that we have a triangle with one side 60.5 feet to the pitcher's mound and the other side 90 feet to first base.

I assumed the bases were in a square pattern, so the angle between 1st and 3rd is 90 degrees.  Assuming this, the angle between the pitcher's mound and 1st base relative to the batter is half of this measurement, which is 45 degrees.

To find the distance, use the law of cosines.  That is,
c^2 = a^2 + b^2 - 2ab*cos(C).
The distance to the mound is a,
the distance to first base is b,
the angle between them is C,
and the distance we are looking for is c.

c^2 = 60.5^2 + 90^2 - 2(60.5)(90)cos(45 degrees)
= 3660.25 + 8100 - 10890*root(2)/2.

That is, c^2 = 11,760,25 - 7707.5 = 4052.8.

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