What are the sides of a right angled isosceles triangle?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.

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