Ratio of Ratios
Geometry
Level
4
\[ \dfrac{2 \sin A + 3 \sin B}{38}=\dfrac{4 \sin B + 5\sin C}{77}=\dfrac{5\sin A + 2\sin C}{53} \]
Let \(A, B, C\) be angles of a triangle that satisfy the condition above.
The ratio \(\cos A : \cos B : \cos C\) is in the reduced form \(x:y:z\) where \(x,y,z\) are positive integers with \(\gcd(x,y,z)=1\). What is the value of \(x+y+z\)?
by
Daniel James Molina