perplexus.info :: Just Math : Given Ratio, Find Sum

Given Ratio, Find Sum (Posted on 2008-01-21)

For a triangle ABC, Area/R=4. Find acosA+bcosB+ccosC.
Note:R is circumradius of triangle ABC.

See The Solution Submitted by Praneeth

Rating: 4.0000 (1 votes)

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re(2): Solution

| Comment 4 of 5 |

(In reply to re: Solution by Praneeth)

If we define

Area(AOB) = (R^2/2)*sin(AOB)

Area(BOC) = (R^2/2)*sin(BOC)

Area(COA) = (R^2/2)*sin(COA)

with AOB, BOC, and COA as directed angles with at least two less than 180 degrees, then this should take care of an obtuse angled triangles.

Posted by Bractals on 2008-01-22 15:10:46

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