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Math Help - Geometry Formulae

  1. #1
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    Geometry Formulae

    The diagram shows part of the frame of a mountain bike. Triangle ABD is an equilateral triangle of side 400mm. BC = DC = 600mm.




    Please help, Thanks

    (i was fooling around with mathtype )
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  2. #2
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    Hello, r_maths!

    You already know that: .cos α = 1/3
    . . Then: .sin α = (2√2)/3

    Since ∆ABD is equilateral, / ABD = 60░.

    Then: .cos(/ ABC) .= .cos(60░ + α)

    . . . . . . . . . . . . . = .cos 60░Ěcos α - sin 60░Ěsin α
    . . . . . . . . - . . - . . - . . . . . . . . . . _
    . . . . . . . . . . . . . = .(1/2)cos α - (√3/2)sin α
    . . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . _
    . . . . . . . . . . . . . = .(1/2)(1/3) - (√3/2)(2√2/3)
    . . . . . . . . . . . . . . . . . . . . . . ._
    . . . . . . . . . . . . . = .(1/6) - (2√6/6)
    . . . . . . . . . . . . . . . . . . . . _
    . . . . . . . . . . . . . = .(1 - 2√6)/6

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  3. #3
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    Thanks Soroban
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