This problem can easily be solved by rotating the x and y axes into x' and y' axes. Because of that, the gravity will have both x' and y' components. Let x' be parallel to the slope and in the same sense as the archer's arrow, and y' be perpendicular to the slope and pointing up. The components of gravity are g_y' = 9.8*sin(15), g_x' = 9.8*cos(15). Also, the arrow is shot at an angle 20+15=35 deg above the x' axis.
The total time it takes for a projectile to stay in air is given by:
T = 2*v_y'/g_y' = 2*50*sin(35)/9.8sin(15) = 22.61 s.
The length traveled by the arrow along the slope is the distance it traveled along the x' axis. x' = 1/2*g_x'*T^2 + v_x'*T.
x' = 1/2*9.8cos(15)*22.61^2 + 50cos(35)*22.61x' = 3346 km.
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