A 30-60-90 triangle is a right triangle having angles of , , and . For a 30-60-90 triangle with hypotenuse of length , the legs have lengths
(1)
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(2)
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and the area is
(3)
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The inradius and circumradius are
(4)
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(5)
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The mean length of a line segment picked at random in a 30-60-90 triangle was computed by E. W. Weisstein (Aug. 5, 2010) as a complicated analytic expression involving sums of logarithms. After simplification, the result can be written as
(6)
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(7)
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(E. Weisstein, M. Trott, A. Strzebonski, pers. comm., Aug. 25, 2010; OEIS A180308).
30-60-90 triangles are used in drafting, as illustrated above. This allows lines of , , , and to be drawn by sliding the drafting triangle along a T-square.