medieval castle puzzle...check the details and help please?

Question

A square medieval castle on a square island was under siege. All around the island, there was 10 metres wide water moat. But the congquerors could make foot-brdiges only 9.5 metres long. Nevertheless a wise man was able to figure out how to get over the water. What do you think was his advice?

Answer 1

One way I can think of:

From one corner, make a 9.5m footbridge across the corner of the moat, from the outer side to the other outer side (ex: from the south side to the east side, with the footbridge going NW)

Then, make a footbridge going from the middle of the first footbridge, to the corner of the wall, sorta like this:

---------------------
....................\....!
......................\..!
...................../..\!
---------------/....!
...................!.....!
...................!.....!

To calculate:
Calculate half the vertical side of First bridge (since you build out of the middle of it) + the vertical side of the second bridge, where both bridges are built at 45 degree angles. This must be 10m or greater to ensure it hits the wall.

sin 45 = opposite / hypotenuse
.707 = opposite / 9.5m
opposite = 6.71

The first footbridge gets you halfway there: 3.36 m. This leaves you 6.64 m from the edge of the castle - so the second footbridge will just barely reach.

Answer 2

Go to a corner of the square moat. Place one of the 9.5 meter planks (or foot-bridges) diagonally across it. Place another plank running from the center of the diagonal plank to the island.

To figure out exactly where to place the diagonal plank, figure that the hypotenuse (diagonal) of the right triangle is 9.5 meters. Work backward - using the Pythagorean Theorem - so that you know you need to place the diagonal 6.71 meters or less from the right angle (the corner of the moat). You can slide the plank out from the corner from both sides at once so it will be equidistant.

Note that this gets you about 4.97 meters out from the corner. You know that the total distance across the corner is 14.14 meters, so just use another 9.5 meters to bridge the resr of the gap - 4.97 + 9.5 = 14.47, enough to bridge a 14.14 meter gap.

(Added more exact detail while keeping the basis of the answer the same)

Answer 3

Place the 9.5 meter bridge across the corner of the moat like so that the bridge makes a triangle at the corner.

then, go to the middle of the bridge and place another bridge with an end on the middle od bridge one and the bank of the island. I can't draw it, but the two bridges will form a T shape.

Answer 4

dig ditches and drain the moat?