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by Anonymous on May 7th, 2009

Anonymous

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Help answer this question below.

If i were to have a roof with a 30 60 90 triangle, the 90 being the roof peak and the bottom side(2a), the left side (a -square root- of 3)and the right side(a). assuming a=3 units how would i figure the distance from the peak to the 2a side? (the bottom)

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Answers. 2 helpful answers below.

  • by Greek2Me on October 23rd, 2009

    Greek2Me

    If you want to understand how this is done, check out these articles for a simple free tool and tutorial that will make trig simple enough for ANYBODY to understand!

    http://www.ehow.com/how_5520340_memorize-trig-functions-losing-mind.html

    http://www.ehow.com/how_5227490_pass-mind-part-unknown-sides.html

    http://www.ehow.com/how_5428511_pass-part-ii-unknown-angles.html

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  • by Quirkie on May 11th, 2009

    Quirkie

    A nice way is to find the area of the triangle using
    Area = half base times height.

    Since the (a) side and the (a sqrt(3)) sides are at right angles, you can take one to be the base and the other the height to get
    Area = (1/2) (a) (a sqrt(3))

    But now if you take the (2a) side to be the base, then you get
    Area = (1/2) (2a) h
    where h is what you want to know.

    The two areas are equal so:
    (1/2) (a) (a sqrt(3)) = (1/2) (2a) h
    a sqrt(3) = 2 h
    (1/2) a sqrt(3) = h

    You could also have used similar triangles, as the perpendicular from the peak makes two more 30-60-90 triangles. The ratios of the sides in the large triangle are the same as the ratios of the three sides in the smaller triangles.

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