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Math Help - triangle

  1. #1
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    triangle

    Suppose a 12 foot ladder is leaning against a wall so that its base is 2 feet from the edge of the wall. As you climb to the very top of the ladder, you find you can reach 7 feet above the top of the ladder. To what height are you reaching in feet, to one decimal place?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by suzdisp View Post
    Suppose a 12 foot ladder is leaning against a wall so that its base is 2 feet from the edge of the wall. As you climb to the very top of the ladder, you find you can reach 7 feet above the top of the ladder. To what height are you reaching in feet, to one decimal place?
    let x be the height that the top of the ladder touches the wall.

    By Pythagoras' theorem. x^2 = 12^2 - 2^2

    you should be able to take it from there

    Hint: the height you can reach is x + 7
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  3. #3
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    Ok, from there I have this so far:


    (x+7)^2=144-4

    (x+7)(x+7)=140

    now what?
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  4. #4
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    to this...
    x^2+7x+49=140.
    now I'm stuck
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  5. #5
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    Quote Originally Posted by suzdisp View Post
    Ok, from there I have this so far:


    (x+7)^2=144-4

    (x+7)(x+7)=140

    now what?
    (x + 7)^2 = 140

    x + 7 = \pm \sqrt{140}

    x = -7 \pm \sqrt{140}
    and discard the negative solution.

    -Dan
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by suzdisp View Post
    to this...
    x^2+7x+49=140.
    now I'm stuck
    Or if you do it this way then
    x^2 + 14x - 91 = 0

    Use the quadratic formula.

    (And note the coefficient on the "x" term. You FOILED this wrong.)

    -Dan
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  7. #7
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    no no no, I hate the quadratic equation. I'll do it your way

    so, I get

    x=-7 +/- SR 140

    x= -7 +/- 11.832159




    so, -7 + 11.832159= 4.8 feet?
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by suzdisp View Post
    no no no, I hate the quadratic equation. I'll do it your way

    so, I get

    x=-7 +/- SR 140

    x= -7 +/- 11.832159




    so, -7 + 11.832159= 4.8 feet?
    Since this is a Math problem I'd use the exact (rather than decimal) answer, but yes, you solved it correctly.

    -Dan
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  9. #9
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    yessssssssss, thank you soooo much for helping me tonight
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by suzdisp View Post
    yessssssssss, thank you soooo much for helping me tonight
    You are welcome, but thank Jhevon. He helped you with the problem, I just helped with solving the equation.

    -Dan
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  11. #11
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by suzdisp View Post
    Ok, from there I have this so far:


    (x+7)^2=144-4

    (x+7)(x+7)=140

    now what?
    where did (x + 7)^2 come from?
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