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

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) (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 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , ,

Square to get .

Square to get .

Combine like terms.

Rearrange the equation.

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

Simplify the square root.

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Answer:

So the solution is which approximates to (when using a calculator).

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

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