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Math Help - Word problem help needed!

  1. #1
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    Word problem help needed!

    Height of a tree

    A woodcutter determines the height of a tall tree by first measuring a smaller one 125ft away, then moving so that his eyes are in line of sight along the tops of the trees, and measuring how far he is standing from the small tree (see figure). Suppose the small tree is 20ft tall, the man is 25ft from the small tree, and his eye level is 5ft above the ground. How tall is the taller tree?


    5ft....................20ft..................talle r tree
    25ft 125ft

    I got 30ft, but I dont think it is right , here is what I did:

    (h/150)(5/25) = 750/25 = 30

    Any help would be greatly appreciated ! thanks!
    Last edited by sallyann; February 3rd 2006 at 11:31 PM. Reason: hit enter
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sallyann
    Height of a tree

    A woodcutter determines the height of a tall tree by first measuring a smaller one 125ft away, then moving so that his eyes are in line of sight along the tops of the trees, and measuring how far he is standing from the small tree (see figure). Suppose the small tree is 20ft tall, the man is 25ft from the small tree, and his eye level is 5ft above the ground. How tall is the taller tree?


    5ft....................20ft..................talle r tree
    25ft 125ft

    I got 30ft, but I dont think it is right , here is what I did:

    (h/150)(5/25) = 750/25 = 30

    Any help would be greatly appreciated ! thanks!
    The triangle from the eye of the wood cutter to the top of the first
    tree to a point 5ft above the base of the tree is similar to the
    triangle from the eye of the wood cutter to the top of the larger
    tree to a point 5ft above the base of the tree.

    The bases of these triangles are 25ft and 150ft respectivly, so as
    they are similar their heights are in the same ratio and the height
    of the first triangle is (20-5)=15ft so the height
    of the second triangle is:

    15 \times \frac{150}{25}=90ft.

    The second tree is 5ft taller than the secon triangle,
    so the tree is 95ft tall.

    RonL
    Attached Thumbnails Attached Thumbnails Word problem help needed!-trees.jpg  
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  3. #3
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