SOLUTION: A 20 foot tall telephone pole is at a right angle with the ground. A 25 foot wire is to be attached from the top of the pole to a point on the ground so the wire is taught. How fa

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Question 78513: A 20 foot tall telephone pole is at a right angle with the ground. A 25 foot wire is to be attached from the top of the pole to a point on the ground so the wire is taught. How far from the base of the pole would the wire be attached?
Thanks~
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
This is a trigonometry problem. They are asking you to solve for one
side of the triangle when two other sides are known.

The Pythagorean theorem is a%5E2%2Bb%5E2=c%5E2 where c is the hypotenuese
(the side of the triangle opposite the right angle) while a and b are
the other sides.

In this case, the hypotenuese (c) is 25 and one of the other sides (a) is 20.

so, via the Pythagorean theorem:
25%5E2=20%5E2%2Bb%5E2
Solve for b:
b%5E2=25%5E2-20%5E2
b%5E2=625-400
b%5E2=225
b=15
An easier way to think about this is to recognize that this is really what we
call a "3-4-5 times 5" right triangle. In other words, one side is 3, another
is 4 and the hypotenuse is 5, all multiplied by 5. If you recognize that, you
right away that the unknown side is just 3*5 or 15.