SOLUTION: Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 9 feet higher than the right bank and the stream is 12 f

Algebra ->  Pythagorean-theorem -> SOLUTION: Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 9 feet higher than the right bank and the stream is 12 f      Log On


   

Question 76911: Two children are trying to cross a stream. They want to use a log that goes from one bank to the other. If the left bank is 9 feet higher than the right bank and the stream is 12 feet wide, how long must a log be to just barely reach?

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
This is a "right triangle" problem.
.
If you measure horizontally from the level of the right bank, the distance across the stream
is 12 feet. But at the point that the horizontal distance reaches the left bank you then
need to go vertically upward 9 feet to get to the edge of the left bank. These two
distances are the legs of a right triangle and are 90 degrees to each other. The length
of the log that goes from the edge of the right bank upward at a slant to the edge of the
left bank is the hypotenuse or long side of the of this triangle.
.
To find the length of the hypotenuse we can use the Pythagorean theorem which says that if
you square the length of each leg of a right triangle and add these two squares, the result
will be the square of the length of the hypotenuse. In equation form this can be written as:
.
a%5E2+%2B+b%5E2+=+c%5E2
.
Where "a" and "b" are the lengths of the legs and "c" is the length of the hypotenuse.
In this problem we can say that "a" is 9 ft, "b" is 12 ft, and c is the unknown length of
the log. Substitute these values into the equation and it becomes:
.
9%5E2+%2B+12%5E2+=+c%5E2
.
Squaring each of the numbers on the left side results in:
.
81+%2B+144+=+c%5E2
.
Add the terms on the left side and you get:
.
225+=+c%5E2
.
And now you can solve for "c" by taking the square root of both sides. When you do that
the equation is reduced to:
.
sqrt%28225%29+=+15+=+c
.
So the log must be 15 ft long to barely reach from the edge of the right bank to the edge
of the left bank.
.
Hope this is an understandable explanation and that you can picture what I have tried to
explain in words. Sometimes it helps to visualize a problem if you make a sketch of the
situation ... in this case showing the width of the stream (12 ft), the difference
in the height of the two banks (9 ft), and the slant distance of the log that goes from
the edge of the lower right bank to the edge of the higher left bank.