# Equilateral Triangle Question

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 .

• what are $B,C$? – Anurag A Jan 8 '17 at 9:15
• Perhaps $ABC$ is an equilateral triangle, and $O$ is inside $ABC$ such that $BO = 3$, $CO = 4$ and $AO = 5$. – JimmyK4542 Jan 8 '17 at 9:28
• Perhaps...and perhaps not. Let's see if the OP explains his own question and, also, adds some work he may have done on it. – DonAntonio Jan 8 '17 at 9:52
• Yes...Its that....JimmyK4542 – DEBOJJAL Jan 8 '17 at 12:48

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.