Where did the RMS Titanic actually hit the iceberg?
The RMS Titanic hit an iceberg on the evening of 14 April, 1912, and sank early in the morning of 15 April, 1912. Titanic's CQD or SOS (distress call) position was 41-56 degrees North and 50-14 degrees West. Titanic's final resting position, over 2000 meters below the surface of the North Atlantic Ocean, is 41-44 degrees North and 49-56 degrees West.
In 1912, navigation at sea could be very imprecise. Obviously, today we have satellite navigation. Back then they used celestial navigation and dead reckoning. The night they struck the berg, there was no moon. In order to accurately compute your position using the stars or the moon, you need to be able to see the horizon through a sextant. Captain Smith may have tried to do this, but he would have been guessing as to the exact sighting of the horizon.
He may have just used what is called the dead reckoned position. Their last accurate fix was probably at twilight when a distinct horizon is available and the stars were visible (we know the sky was clear that night). That means they had to rely on their recordings of ship course and speed to compute their position from their last accurate position (which was probably 5 hours old).
What Captain Smith probably did was use a combination of the two methods. He probably split the difference between a celestial fix and a dead reckoned position. This is only conjecture.
See also Titanic Facts.
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