Why maths counts part three

Due to some unexpected circumstances you and your work mate find yourselves on a deserted island. Unfortunately, the island is covered in deep holes that look much like rabbit holes.  You have peered down them but are a bit chicken to go poking sticks down there.

Alarmingly, you find out the first night that the holes are occupied by man-eating crabs.  The crabs emerge, attack on mass and drag your fellow companion down the holes - In bits.  Brian paid the ultimate price for you to have one extra day alive.  However, tonight they are coming for you.

You must get off the island before dark.

As you stand on the shore you notice an island off in the distance.  It looks beautiful and safe.  You wonder how far it is?  Could you swim to it?  How far is too far?  Very hard to judge distances on the sea.

The non-maths scenario

You find the of idea avoiding being eaten by crabs quite motivating.  Yet, it's hard to tell how far that island it.  It could by one kilometer or it could be four.  It would suck to get halfway and run out of gas.

You hope for the best and start swimming....

It turns out your distance estimation was quite wrong.  The island never seems to get any closer while your own island gets smaller every second.  Lets just say, it doesn't end well.

The 'I'm pretty awesome at problem solving scenario'.

Actually, I'm not going to describe this one.  I'm going to ask you instead - Is it possible to work out how far away the island is?  Is it possible to work it out within a reasonable range of accuracy?

I think it is possible.  My technique involves fashioning a 45° ruler (which you could make from sticks right?) and applying a bit of creative thinking.  With a little MacGyver'ing' you could do it.

I would love your ideas or your kids ideas - especially the older kids.  Please ask you kids (show them the picture) and see what they say.  It may surprise you.

This might help to get the juices flowing - can you work out how high a tree is from the ground - without climbing it?  (Yes you can).


Think trigonometry.  But even if you don't know trig you can still work it out.

I would love to know how people would work out far away the island is.

Good luck - I'll post my answer in a day or two.