SOLUTION: A wire reaches from the top of a 13-meter telephone pole to a point on the ground 9 meters from the base of the pole. what is the length of the wire to the nearest tenth of a meter

Algebra ->  Trigonometry-basics -> SOLUTION: A wire reaches from the top of a 13-meter telephone pole to a point on the ground 9 meters from the base of the pole. what is the length of the wire to the nearest tenth of a meter      Log On


   

Question 551263: A wire reaches from the top of a 13-meter telephone pole to a point on the ground 9 meters from the base of the pole. what is the length of the wire to the nearest tenth of a meter?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are 13 and 9 this means that a=13 and b=9


Also, since the hypotenuse is x, this means that c=x.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


13%5E2%2B9%5E2=x%5E2 Plug in a=13, b=9, c=x


169%2B9%5E2=x%5E2 Square 13 to get 169.


169%2B81=x%5E2 Square 9 to get 81.


250=x%5E2 Combine like terms.


x%5E2=250 Rearrange the equation.


x=sqrt%28250%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=5%2Asqrt%2810%29 Simplify the square root.


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Answer:


So the solution is x=5%2Asqrt%2810%29 which approximates to x=15.811 (when using a calculator).


This means that the length of the wire is approximately 15.8 meters.