rational expressions/pythagorean theorem (guy wire)

[traceylsambrose]

A guy wire of length 50 feet is attached to the ground and to the top of an antenna. The height of the antenna is 10 feet larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground. What is the height of the antenna?

I'm really not sure how to set this up... your help is appreciated.

Thanks, Tracey

 

[stapel]

A good start would be to draw the triangle. Then label the height, the base (in terms of the height), and the hypotenuse.

Eliz.

 

[soroban]

Re: rational expressions/pythagorean theorem

Hello, Tracey!

Did you make a sketch?

A guy wire of length 50 feet is attached to the ground and to the top of an antenna.
The height of the antenna is 10 feet larger than the distance from the base of the antenna
to the point where the guy wire is attached to the ground.
What is the height of the antenna?

        *
        | \
        |   \
        |     \50
  x + 10|       \
        |         \
        * - - - - - *
              x

Now apply Pythagorus . . . and solve for \(\displaystyle x.\)

Note that the height of the antenna is \(\displaystyle x\,+\,10\)

 

[traceylsambrose]

rational expressions/pythagorean theorem

k-thanks
would it look something like this?
50 squared = x squared + (x+10) squared

 

[tkhunny]

That would be it. Now solve for 'x'.

 

[Denis]

Re: rational expressions/pythagorean theorem

50 squared = x squared + (x+10) squared

Next time, post this way: 50^2 = x^2 + (x+10)^2