I need to calculate the altitude of a regular triangle (equilateral) but i only have the radius (polygon radius) available (). I have been searching for formulas (i am not a mathematically inclined person) but i could not find any. Also a search on mathematics yielded no results. I did find a formula for finding regular triangle altitudes when the side length is known, here: However, in my case, side length is unknown. Is it possible to find the altitude and if so, how? Thanks!
Michael
$\endgroup$1 Answer
$\begingroup$The altitude is 3/2 of the radius, $r$.
Draw an upright triangle, with a radius line from the center, $C$, to the lower right vertex, $V$. Drop a perpendicular from the center to the midpoint $M$ of the bottom edge. This is a 30-60-90 triangle, so its hypotenuse is twice the short leg, i.e., the polygon radius is twice the distance $CM$.
But the line from the top vertex $T$ to the opposite midpoint $M$ is divided in a ratio of 2/3 to 1/3 by the center $C$, i.e., $TC$ is twice $CM$. Since $CM = r/2$, we have $TC = r$ and thus $TM$, the altitude, is $3r/2$.
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