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Math Help - More Missing Lengths

  1. #1
    Newbie
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    Nov 2011
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    6

    More Missing Lengths

    Well done!

    Heres a harder one!

    Part of a lifting device is shown in the diagram below. The longest member is called a tie bar and is angled at 70 to the horizontal. The other long member is called the strut and is angled at 80 to the horizontal. The length of the base is 1.4 m. (Find all the missing lengths & angles)

    More Missing Lengths-untitled.png
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  2. #2
    Junior Member mathbyte's Avatar
    Joined
    Oct 2011
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    Re: More Missing Lengths

    Well, we know the angle between the longer members is 10 degrees, because of the angles of the members to the horizontal.
    We also know the larger acute angle in the triangle is 70 degrees; this too comes from the given information.
    This the obstuse angle is 180 - 70 - 10 = 100 degrees.
    By the law of sines, 1.4/(sin 10) = (strut)/(sin 70) = (tie bar)/(sin 100)
    Thus, the tie bar is about 7.940 m long, and the strut is about 7.576 m long.
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