In a equilateral triangle ABC , $3$ Rods of length $3 , 4 , 5$ units are placed such that they intersect at a common point $O$ and other end being on the vertex A,B,C respetively.. Find the angle $BOC$, if $BO=3$ units and $CO=4$ units .
Equilateral Triangle Question
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$\begingroup$
geometry
coordinate-systems
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0what are $B,C$? – 2017-01-08
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0Perhaps $ABC$ is an equilateral triangle, and $O$ is inside $ABC$ such that $BO = 3$, $CO = 4$ and $AO = 5$. – 2017-01-08
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0Perhaps...and perhaps not. Let's see if the OP **explains** his own question and, also, adds some work he may have done on it. – 2017-01-08
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0Yes...Its that....JimmyK4542 – 2017-01-08
1 Answers
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HINT.
Use the cosine rule to obtain two equations for $x=\cos(\angle BOC)$ and $y=\cos(\angle AOC)$. Remember that $$ \cos(\angle AOB)=\cos(2\pi-\angle AOC-\angle BOC)=\cos(\angle AOC+\angle BOC)=xy-\sqrt{1-x^2}\sqrt{1-y^2}. $$ You'll get in the end a third degree equation for $x$, which has a rational solution easy to find and can thus be factorized.