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Math Help - Hexagon Angles/Trig.

  1. #1
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    Hexagon Angles/Trig.

    Hey guys, I have this assignment due on Monday and I have done all of it except for the last question. I am in Year 10 level 1 Maths.

    Here is the questions.

    Mr X is constructing a hexagonal pergola in his backyard. The roof of the pergola needs to be 7 metres wide (from one side to its opposite, not vertex to vertex). The top view of the pergola is a regular hexagon and is shown in the diagram below.



    A) Calculate the interior angle of each vertex of the pergola.
    Notes: Ok I think this has to do with the sin/cosine rule, but I just don't know the equations for this.

    B) Using the cosine rule and not the tangent ratio, calculate how long each side must be to achieve an overall width of 7 metres as stated above.
    Notes: I have no idea about this question.

    C) If Mr X placed guttering around the perimeter of the roof, what is the minimum length of guttering required?
    Notes: No idea aswell :|

    Yeah so I pretty much need help with these, if someone can try and do it, I thank you.

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  2. #2
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    A) no cosine/sine rule here..

    use this:
    [(n-2) * 180]/n = angle of 1 vertex = x
    n = number of vertices (6)

    B) draw lines from each vertex to the center of hexagon so you'll see the triangles.
    all sides of a chosen triangle are the same length = a

    ((a^2 = a^2 + a^2 - 2 * a * a * cos (x/2)
    x = the angle you calculated in A) section. << just to show the cosine rule.. you get nothing from that without knowing a))

    better way is to use this.. 2 * [(a * sqrt (3))/2] = 7
    you can compare the results.. should be the same.


    C) what's a guttering? xD
    hmm.. 6a?
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  3. #3
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    C is pretty much asking to find the smallest perimeter possible with your answers to B. I think.
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  4. #4
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    C) is 6a then.

    and I remembered another way for B)
    c = 7
    c^2 = a^2 * a^2 - (2 * a * a * cos (x))
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  5. #5
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    attachment..
    Attached Thumbnails Attached Thumbnails Hexagon Angles/Trig.-hexagontq1.png  
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