The skipper of a boat knows that the water is too shallow
to bring his boat inside a “danger semicircle” that
goes from lighthouse to lighthouse. How can the angle
between his sightings of the two lighthouses help him
decide when he is entering the danger zone?
The angle subtended on a diameter of a circle is always 90º.
So if we consider the line between the two lighthouses to be a diameter of a semicircle, then as long as the angle formed by the two lines of sight to the lighthouses is less than 90º the skipper will be outside the semi-circle.
If the angle is greater than 90º .....