I have above triangle but actually it is on earth.
in general BC = AB *Sin y
but in my situation A, B and C are gps coordinates and I want to find true distance between B and C.
So far I know AD, AB, z and y angles.
I know the world radius which is 6,371 km or 6,371,000 m
I am using WGS-84 coordinates as well.
Point Coordinates:
A => Lat: 49.81666666666667 , Lon: -2.75
D => Lat: 50.493333333333332 , Lon: 0.98666666666666669
B => Lat: 50.028766666633331 , Lon: -1.75
AB = 40.729078462466845 Nautical Miles
y => 4.3753712076250508 degrees
From the spherical law of sines you get
\begin{align*} \frac{\sin\tfrac\pi2}{\sin\frac{AB}R}&=\frac{\sin y}{\sin\frac{BC}R}\\ \sin\frac{BC}R&=\sin\frac{AB}R\cdot\sin y\\ BC&=R\cdot\arcsin\left(\sin\frac{AB}R\cdot\sin y\right) \end{align*}
This is assuming the earth is a sphere, not the more complicated WGS-84 ellipsoid.
It might be educating to see how the Euclidean law of sines gives rise to the formula you quoted.