# Competition problem

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#### LAZ

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
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.

topsquark

#### topsquark

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

-Dan

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