If we want to sketch a triangle with angle of 45-45-90 we know that it's a right triangle, because of the 90º angle
the we can use the trig relationships:

And:

By pytagoras:

Where l and L are the two legs, since the angles are equal, l and L are equal:

Then:
![\begin{gathered} (1)/(h)=\sin (45) \\ h=\sqrt[]{2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/3vth6d8p1dgbfppj6noqimeduz34b1c87m.png)
By pythagoras:
![\begin{gathered} (\sqrt[]{2})^2=((1)/(\sin(45)))^2+((1)/(\cos 45))^2 \\ 2=1+1 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/wqk2p0832ppq1mnjon8liaucwp4hy1yk0l.png)
Then we know that the length og each side is √1 which is 1, and then added to the other leg, 1 + 1 = 2
By the angles 45º, 45º and 90º and one leg of length 1, the sides are 1, 1 and 2