SOLUTION: in a45 degree - 45 degree - 90 degree triangle, the ration of the length of the hypotenuse to the lengh of a side is?

Algebra ->  Pythagorean-theorem -> SOLUTION: in a45 degree - 45 degree - 90 degree triangle, the ration of the length of the hypotenuse to the lengh of a side is?      Log On


   



Question 549212: in a45 degree - 45 degree - 90 degree triangle, the ration of the length of the hypotenuse to the lengh of a side is?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
In this kind of right triangle, the two legs are the same length, let's call it x and the hypotenuse is c.
From the Pythagorean theorem, we get:
c%5E2+=+a%5E2%2Bb%5E2 but a = b = x, so...
c%5E2+=+2x%5E2 and...
C+=+sqrt%282%29x
The ratio of the hypotenuse (c) to one leg is just:
c%2Fx but c+=+sqrt%282%29x so we get...
sqrt%282%29x%2Fx+=+sqrt%282%29