Maths Help?

Discussion in 'Community Discussion' started by cambookpro, Apr 30, 2013.

  1. cambookpro, Apr 30, 2013
    Last edited: Apr 30, 2013

    cambookpro macrumors 603


    Feb 3, 2010
    United Kingdom

    I remember asking maths questions here before and getting great responses, so though I might as well try again.

    As a school/individual we're meant to be gifted and talented and all that crap, but still manage to get stumped a lot of the time! :p

    Anyway, we've been doing trigonometry in 3D and was wondering if somebody could answer a few questions I have?

    I've attached both the question and my workings out below, however am having a hard time differentiating between 3b and 3d, and also 3c and 3e. Any enlightenment you can bring would be much appreciated. I seem to be garnering the same answers for both, when I'm sure that shouldn't be the case?

    May just be a stupid mistake that I've overlooked, but hey ho.

    Feel free to post any maths ( ;) ) queries you have here as well, for some community help.

    Ignore me using 12 instead of 21, I changed that after I copied the question wrong... :eek:

    Attached Files:

  2. cambookpro thread starter macrumors 603


    Feb 3, 2010
    United Kingdom
    Silly me...

    The diagonal is not the same!

  3. chown33 macrumors 604

    Aug 9, 2009
    Sailing beyond the sunset
    I interpret "slant edge" to mean one of the edges with an endpoint at E. I wouldn't call any of the base edges a "slant edge", but I'm in the US, you're in the UK, and I have no idea if that could be important.

    So a "slant edge" would be one of the edges EA, EB, EC, or ED. They're identical in length because it's a right pyramid.

    The line EV would NOT be a "slant edge", because EV is not an edge.

    If we assume my interpretation of "slant edge" is correct, it's still unclear to me what 3e is asking for. It could be the angle EBU (or ECU, etc.), or it could be the angle EBA (or EBC, etc.). Either one could be seen as fitting the description of 3e. I would probably calculate both, label them clearly in my answer, and then write a brief note that the question could use some clarification.
  4. Don't panic macrumors 603

    Don't panic

    Jan 30, 2004
    having a drink at Milliways
    EV is the distance between the vertex and the middle of one of the sides at the base, the slant edge connects the vertex E to one of the corners of the base (like EB).
    same with the angles (EVU vs EBU).
  5. dommeister, Apr 30, 2013
    Last edited: Apr 30, 2013

    dommeister macrumors member

    Apr 27, 2009
    a) Volume = 1/3 x Area of base x height
    = 1/3 x 42mm x 42mm x 68mm
    = 39 984 mm^3

    b) Pythagoras Theorem
    c^2 = a^2 + b^2
    where c = EV, a = EU b= UV
    c = √(68^2 + 21^2)
    c = √ (5065mm^2)
    c = 71.16881mm
    EV = 71.16881mm

    c) Angle EVU = arc tan or tan^-1 (opposite/adjacent)
    Opposite = line EU Adjacent = line UV
    Angle EVU = tan^-1 (68mm/21mm)
    Angle EVU = 72.838 degrees or 1.27126434 radians

    d) Pythagoras Theorem to find length UB
    c2 = a2 + b2
    where c = UB a = UV b = UW where W = midpoint of line AB
    c = √(21^2 + 21^2)
    c = 29.69848mm
    UB = 29.69848mm

    Pythagoras Theorem to find length EB
    where c = line EB a = line EU b = line UB
    c^2 = a^2 + b^2
    c = √(68^2 + 29.69848^2)
    c = 74.20243mm
    EB = 74.20243mm

    e) Angle EBU
    Find BU length using Pythagoras theorem
    where c = UB a = UV b = UW where W = midpoint of line AB
    c^2 = a^2 + b^2
    c = √(21^2 + 21^2)
    c = √ (882mm^2)
    c = 29.69848mm
    line UB = 29.69848mm

    Angle EBU = arc tan or tan-1 (opposite/adjacent)
    where opposite = EU @ 68mm, adjacent = UB @ 29.69848mm

    = tan-1 (68mm/ √ (882mm^2) )
    Angle EBU = 66.4070684 degrees or 1.15902199 radians

    f) Side length of cube = Cube root or 3√ volume of pyramid from answer a)
    = 3√ 39 984 mm^3
    = 34.19496 mm

    Round off or convert the units to cm in the answers if necessary . :)

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