in a 45, -45, -90 degree triangle the ratio of the length of the hypotenuse to the length of the side is

Question

in a 45, -45, -90 degree triangle the ratio of the length of the hypotenuse to the length of the side is

Answer 1

This is an isoceles triangle. It also has a right angle. Therefore if c is the hypothenuse then

 

a² + b² = c² However since a = b  then  2a² = c² which means that  c = √2*a so the ratio of the length of the hypothenuse to the length of the side  is c/a = √2

Answer 2

An Isoceles Triangle has  two legs equal in length.

       

       leg1 = leg2 = a 

  

      leg1/ lege2 = 1

 

    Hypotenuse = leg1 ^2  + leg2 ^2 =  2a^2

 

      Hypotenuse = c

 

       Pythagoras theorem : c^2 = 2a^2        c =a √2 

 

        Hypotenuse / leg 1 = hypotenuse/ leg 2 = a√2 / a = √2

  

         leg1/ hypotenuse = leg2 / hypotenuse = a/ a√2 = 1/√2 = √2/2

 

     These ratios constitute trigonometric functions of 45°