Monday, June 11, 2012

When given the lengths of two sides of a right triangle, we can obtain the third side by using the Pythagorean Theorem.

a^2 + b^2 = c^2, where c is the length of the hypotenuse.

A Pythagorean triple consists of 3 integers which satisfies the Pythagorean Theorem.

There are 12 such triples in which c < 100. For all practical purposes you need not memorize all of theses, but many times the tiples up to (11, 60, 61) are seen frequently. It helps to memorize those.

( 3 , 4 , 5 )( 5, 12, 13)( 7, 24, 25)( 8, 15, 17)
( 9, 40, 41)(11, 60, 61)(12, 35, 37)(13, 84, 85)
(16, 63, 65)(20, 21, 29)(28, 45, 53)(33, 56, 65)
(36, 77, 85)(39, 80, 89)(48, 55, 73)(65, 72, 97)
                     

2 comments:

  1. Pythagoras theorem is very helpful to calculate the hypotenuse,altitude and base of right angle triangle.But I think that Hero's formula is also applicable in these cases.
    Product Rule

    ReplyDelete
  2. Yes, I remember the product rule used in Calculus. Very interesting approach and thanks for the reply!

    ReplyDelete