From any vertex, he puts each end of one plank slightly less than about √[361/2] ft from this vertex so that both ends are supported on dry land.
Then he carries the other plank to the middle of this one and lays it down so that it connects with the corresponding vertex of the island......at the middle of this first plank, he is √[361 /4] ft from the beginning vertex......and the distance from this vertex this point to the island is slightly more than [20√2 - √[361/4] ft = 18.784 ft.......so it can be easily be spanned by the other 19 foot plank......!!! {i.e, he stays dry.....}
Here's a pic of the situation starting from the lower left vertex..... AB is the first plank, CE is the distance from the middle of this plank to the island vertex.....

