Altitude of a Tetrahedron Given Its Edges

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This Demonstration constructs an altitude of a tetrahedron given its edge lengths
,
,
,
,
,
,
. (In the figure, the edge length of
is
.) Suppose the altitude is from vertex
to the opposite face
. First, construct the net of
with the triangle
in the center (unfold completely). Normals from the vertex
to the sides
,
,
meet at a point
. This is the 3D orthogonal projection of vertex
. In 3D, the lines
,
and the altitude form a right triangle with
as its hypotenuse. So we can construct the altitude as a leg of the triangle.
Contributed by: Izidor Hafner (March 2017)
Open content licensed under CC BY-NC-SA
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"Altitude of a Tetrahedron Given Its Edges"
http://demonstrations.wolfram.com/AltitudeOfATetrahedronGivenItsEdges/
Wolfram Demonstrations Project
Published: March 27 2017