(1) He sees the hypotenuse of a right triangle made by the deck, the mast and the front edge of the beam moving down to the deck.

(2) Can we have any other Pythagorean triangles with a Fibonacci number as the hypotenuse (the longest side)?

(3) In case you have forgotten your high school geometry, the hypotenuse is the side opposite the right angle.

(4) In fact it is the length of the hypotenuse of a right angled triangle which had sides of length one.

(5) The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the legs.