What are the sides of a right angled isosceles triangle?

Expert Answers
hala718 eNotes educator| Certified Educator

Let  abc be an isoscele right angle triangle, such that:

ab = bc

angle b = 90

Since ab = bc , then angle a = angle c

But angle a + angle c = 90

==> angle a = angle c = 45

We know that:

 cosa = cos45

          = sqrt2/2 = adjacent/hypotenuse

          =  sqrt2/2 =  ab/ac

==> ab = bc = sqrt2.....(sides)

==> ac (hypotenuse) = 2

                                                  

 

neela | Student

Since the right angled triangle is isoscles, we assume  that its equal sides are the right angle making sides.

So applying the Pythagoras Theorem, the hypotenuse h should be.

h = sqrt (x^2+x^2) = sqrt(2x^2) = (sqrt2)x.

So any triangle with sides, (x , x and  (2^(1/2)x  for any value of x should represent a right angled triangle.

Also we can say if the ratio of the length of three sides of triangle are 1:1:2^(1/2) , then the triangle is a right angled triangle.