I wanted to find out how tall the rugby posts at my local stadium were. Taking a handy rod as my standard unit of length, I went out to the field with the rod and a gadget for measuring angles from ground level.

I walked out 10 rods from one of the goal posts and measured the angle from the ground to the top of the post. Then, just to be certain my calculations would be as accurate as possible, I walked another 10 rods in the same direction, and measured the angle again. To be absolutely precise (as I'm a bit of a perfectionist), I walked a final 10 rods in the same direction and measured the angle a third time.

When I went home to calculate the height of the goal post, I was surprised to discover that the sum of my three angles was precisely a right angle.

How tall were the goal posts in rods?

I'm brazilian, math and logic are my passion.

Twenty years ago, more or less, I read about this problem in a american scientific magazine. It was presented with no solution, but in its formulation, (I still have its formulation), it is tacitly said that this can be proved WITHOUT THE USE OF TRIGONOMETRY, using only a "geometrical approach".

I never succeeded in obtaining the proof.

Perhaps, although the answer is yet given (using trigonometry is too easy), my proposal to SAM is (if it is possible) to continue with the challenge, with this new observation.  

Edited on March 11, 2005, 6:05 pm

Posted by pcbouhid on 2005-03-11 14:46:46