Competition problem

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LAZ

Nov 2019
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0
IL
Can anyone help with this problem?

Located inside equilateral triangle GHJ is a point M such that GM =13, HM =18 , and JM = 20 . Rounded to the nearest degree, find the degree measure of ∠GMJ .
 

Walagaster

MHF Helper
Apr 2018
223
144
Tempe, AZ
Label angle GMJ as $a$ and the other two central angles $b$ and $c$. Call each side of the triangle $s$. You know $a+b+c=360$. Apply the law of cosines to each of the three sub-triangles to get three equations for $s$ in terms of the given lengths and angles $a,~b,~c$. You then have four equations in four unknowns $s,~a,~b,~c$. Have fun.
 
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topsquark

Forum Staff
Jan 2006
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That sounds like some good general advice for a competition problem.

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-Dan
 
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