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Isosceles Right Triangle


IsoscelesRightTriangle

A right triangle with the two legs (and their corresponding angles) equal. An isosceles right triangle therefore has angles of 45 degrees, 45 degrees, and 90 degrees. For an isosceles right triangle with side lengths a, the hypotenuse has length sqrt(2)a, and the area is A=a^2/2. The hypotenuse length for a=1 is called Pythagoras's constant.

Polyforms made up of isosceles right triangles are called polyaboloes.

IsoscelesRightTriangleIIsoscelesRightTriangleO

The inradius r and circumradius R are

r=1/2(2-sqrt(2))a
(1)
R=1/2sqrt(2)a.
(2)

Triangle line picking for points in an isosceles right triangle with edge lengths a, a, and sqrt(2)a gives a mean line segment length of

l^__(Delta(a,a,sqrt(2)a))=1/(30)[2+4sqrt(2)+(4+sqrt(2))sinh^(-1)1]a
(3)
=1/(60)(4+8sqrt(2)+sqrt(2)cosh^(-1)3+8sinh^(-1)1)a
(4)
=0.414293...a.
(5)

See also

30-60-90 Triangle, Isosceles Triangle, Polyabolo, Right Triangle

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Cite this as:

Weisstein, Eric W. "Isosceles Right Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IsoscelesRightTriangle.html

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