30-60-90 Triangle
A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths
and the area is
| A=1/2bc=1/8sqrt(3)a^2. |
(3)
|
The inradius r and circumradius R are
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
(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 0 degrees, 30 degrees, 60 degrees, and 90 degrees to be drawn by sliding the drafting triangle along a T-square.
See also
Isosceles Triangle, Polydrafter, Right Triangle, Triangle, Triangle Line PickingExplore with Wolfram|Alpha
References
Sloane, N. J. A. Sequence A180308 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
30-60-90 TriangleCite this as:
Weisstein, Eric W. "30-60-90 Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/30-60-90Triangle.html