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Math Help - Solid trigonometry issue..

  1. #1
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    Solid trigonometry issue..

    I have attached the question and the diagram. I was able to find answer for a, but need help with the rest.

    I just can't seem to figure out how to solve b. As you see, this is a GCSE level question, you'll have to be a bit basic here.

    Thanks
    Attached Thumbnails Attached Thumbnails Solid trigonometry issue..-trig_issue.jpg  
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  2. #2
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    #b Is angle EFH, which is 90 - angle CFH.

    Consider the right triangle CFH, CH is 10 and FH is 20, both given:

    sin CFH = 10/20 = 1/2

    So, 90 - sin^-1 (1/2) =

    For # c and # d.

    Angle ACB = BAC = 70 degrees

    The length line from the mid-point of AC to the mid-point of GH is the length of the line from the mid-point of AC to B minus the length of the line from the mid-point GH to B:

    14sin(70) - 4sin(70) = 9.397

    Together with the line joining the mid-points of AC and DF, 10sqrt(3) = 17.321, from #a, and the line joining the mid-points of DF and GH you have a right triangle.

    #c tan^-1 (17.321/9.397) =

    #d Using the same triangle: (9.387)^2 + (17.321)^2) = 3888.302

    sqrt 388.302 =

    I hope this helps. I hope it's correct.
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  3. #3
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    Thanks. But I still didn't understand #c and #d ... I just don't get what I have to do there despite wasting another hour on it ...
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  4. #4
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    Sorry that didn't help. Does this.



    Use the white right triangle. Angle C is for #c, it corresponds to the one asked for.

    Then find the hypotenuese for #d.
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  5. #5
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    Thanks a lot got it now.

    This part is new to me though:

    14sin(70) - 4sin(70) = 9.397

    On what basis can we do this. Is it because GB is 4cm in length and GH || AC?
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  6. #6
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    Triangle ABC is isosceles so its height, the perpendicular from the midpoint of AC to the vertex B, is given by:

    <br />
sin(70) = \frac{Opp}{Hyp}<br />

    <br />
sin(70) = \frac{Opp}{14}<br />

    14 * sin(70) = Opp

    Yes, triangles ABC and BGH are similar so the line joining the midpoints of AC and GH is:

    <br />
14 * sin(70) - \frac{4}{14} * 14 * sin(70) = 14 * sin(70) - 4 * sin(70)<br />
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