A Pythagorean triple is 3, 4, 5 since 32 + 42 = 52. By using this as a ration (3 : 4 : 5), it can be quite useful:
To make a right angle for building purposes (just like the ancient Egyptians), getting three lengths in the ratio of 3 : 4 : 5 (say 30 cm, 40 cm and 50 cm) joining them to make a triangle will create a right angle where the sides with the ratio of 3 : 4 join.
While doing your homework, or on mapping, or for distance.
Carpentry
In comparing the effect of focal lengths in digital cameras with different sized sensors.
Sometimes when turning a corner you have walk through 90 degrees or crossing a rectangular field you'd take the shortest distance across it which is its hypotenuse.
they are no uses
While doing your homework, or on mapping, or for distance.
it can be used when adding up the sides of a computer toaster
You work as a house painter. When you set up your ladder, you like to set the base 5-ft from the wall, for stability. How high on the wall can you reach with a 12-ft ladder ? With a 15-ft ladder ? With a 30-ft ladder ? ============================================================== The question is not: Can the Pythagorean Theorem help you in real life ? The question is: Is your life real enough yet that you can use the Pythagorean Theorem to make it easier ?
In real life its not useful, unless you're going to need geometry in the career you choose.
Carpentry
In comparing the effect of focal lengths in digital cameras with different sized sensors.
You don't, unless you work in engineering. The Wikipedia article on "binomial theorem" has a section on "Applications".
shopping, travel, measurements and money are the real life applications of real number system.
when simplifying fractions
Any pythagorean triangle with unequal legs.
Yes if it was not practical it was not there. You can see the real life use on this link http://www.intmath.com/Applications-differentiation/Applications-of-differentiation-intro.php
There are no real life applications of reciprocal functions