Howdy lammah-ga,
First, we have to figure the proper placement of the ladders to make
this work. The first ladder has to be placed at a diagonal at one of
of the corners of the moat.
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Unlike the depiction above, the result should form a isosceles right
triangle.
The second ladder is placed from the middle of the first ladder in a
perpendicular to the first ladder to the closest corner of the island of
land.
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We know from the Pythagorean theorem the distance from an outside corner
of the moat to the closest outside corner of the island is the square root
of 11 feet squared plus 11 feet squared, or around 15.5563 feet.
The distance from the outside corner of the moat to the center of the
first ladder is equal to 1/2 of the length of the ladder, or 5 feet.
If we do the calculation of 15.5563 feet - 5 feet we get 10.5563 feet,
so the 10 foot ladders are not long enough.
From the above, the distance from an outside corner of the moat to the
closest outside corner of the island can also be described as the length
of a ladder plus 1/2 the length of that ladder, or 3/2 of the ladder
length.
If we take our 15.5563 foot distance from an outside corner of the moat to
the closest outside corner of the island and multiply it by the inverse
of 3/2, or 2/3, we get a needed ladder length of 10.371 feet.
10.371 feet + 1/2 of 10.371 feet = 15.5565 feet, which with rounding is
real close to the actual number needed. You should do the calculations
without the rounding to get figures as accurate as needed.
The problem as outlined does not provide the width or shape of the ladders,
so the stability of using these lengths of ladders would not be stabile in
the configuration outlined above.
If you need any clarification, please feel free to ask.
Search strategy: I did the calculations myself.
Looking Forward, denco-ga - Google Answers Researcher |