A fisherman wants to catch a fish 5 m away horizontally and 2 m below the rod tip. How long should the line be?
Try this
5
line length = √(distance² + 2²) = 5.39
It's a right triangle
The rod tip, the spot above the fish, and the fish itself form a right angle at the surface. The horizontal reach and the depth are the two legs; the line is the hypotenuse — so line² = reach² + depth².
Maths gives the minimum straight-line length. In real life add slack for the cast, the current's pull, and the fight — but you now know the floor.
Your turn
The fish is 8 m away horizontally and 6 m below the rod tip. Shortest line?
Pythagoras
line = √29 ≈ 5.39 m
Real fishing also needs slack and current correction. Maths gives the minimum; experience adds the rest.