Formula for the length of line that connects two sides of a triangle.

Question

For the triangle in the picture, coordinates of $A$, $B$ and $C$ are known. Is there an explicit formula for length $XY$, as a function of height $h$? It's a function of other variables as well, but it's important that it depends explicitly on $h$. enter image description here

$XY$ is parallel to side $c$, but I'm not good at drawing.

Yes, try doing it for a right angled triangle first, and remember the length of the base is $|A-B|$. — copper.hat, Oct 23 '13 at 18:09

score 2 · Accepted Answer · answered Oct 23 '13 at 18:11

2

$Cxy$ is similar to $CAB$, so the sides are in the same ratio as the altitudes.

answered Oct 23 '13 at 18:11

Ross Millikan

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Formula for the length of line that connects two sides of a triangle.

1 Answers1