Magnetic reconnection transfers energy from magnetic fields to particles in space, but the conditions under which reconnection is initiated are not well understood. Indirect evidence confirms the existence of reconnection where merging fields are anti-parallel, but also confirms the existence of another type of reconnection, called component reconnection. This ambiguity has resulted in considerable debate over which of these types of reconnection dominates. Here we report on a method using 3D plasma observations from the TIMAS instrument on Polar as it passes through the northern cusp to calculate the distance to the reconnection line, and subsequently trace this distance to the magnetopause. Results from 130 events reveal that in general, magnetic reconnection occurs along an extended line across the dayside magnetopause, consistent with the component reconnection scenario. These results indicate that reconnection in other regions of space (e.g., solar flares, Earth's magnetotail) should not be limited to anti-parallel magnetic field geometries.