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Math Help - trig problem solving

  1. #1
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    Exclamation trig problem solving

    When an extension ladder rests against a wall it reaches 4 m up the wall. The ladder is extended a further 0.8 m without moving the foot of the ladder and it now rests against the 1 m further up. Find:
    a) the length of the extended ladder

    please show alll working out.
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  2. #2
    A Plied Mathematician
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    A cute problem. What steps have you taken so far?
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  3. #3
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    Not sure if i'm reading this correctly but if the ladder is extended 0.8m, how can it be 1m further up the wall?
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  4. #4
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    Hello, Tessarina!

    When an extension ladder rests against a wall it reaches 4 m up the wall.
    The ladder is extended a further 0.8 m without moving the foot of the ladder
    and it now rests against the 1 m further up.

    a) Find the length of the extended ladder.

    The original length of the ladder is L meters.
    The foot of the ladder is x meters from the wall.
    The ladder reaches 4 meters up the wall.

    Code:
          *
          |\ 
          | \
        4 |  \ L 
          |   \
          |    \ 
          * - - * 
             x
    We have: .x + 4 = L . . x = L - 16 .[1]



    When the ladder is extended to a length of L + 0.8 meters,
    . . it reaches 5 meters up the wall.

    Code:
          *
          |\ 
          | \
        5 |  \ L + 0.8
          |   \
          |    \ 
          * - - * 
             x
    We have: .x + 5 = (L + 0.8) . .x = (L + 0.8) - 25 .[2]



    Equate [2] and [1]: .(L + 0.8) - 25 = L - 16

    . . (L + 0.8) - L = 25 - 16 . . 1.6L = 8.36

    . . L = 8.36 1.6 . . L = 5.225


    The length of the extended ladder is: .5.225 + 0.8 = 6.025 meters.

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