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:
[tex]\sin (45º)=\frac{1}{h}[/tex]And:
[tex]\cos (45º)=\frac{1}{h}[/tex]By pytagoras:
[tex]h^2=l^2+L^2[/tex]Where l and L are the two legs, since the angles are equal, l and L are equal:
[tex]\begin{gathered} \cos (45)=\frac{1}{h} \\ \sin (45)=\frac{1}{h} \end{gathered}[/tex]Then:
[tex]\begin{gathered} \frac{1}{h}=\sin (45) \\ h=\sqrt[]{2} \end{gathered}[/tex]By pythagoras:
[tex]\begin{gathered} (\sqrt[]{2})^2=(\frac{1}{\sin(45)})^2+(\frac{1}{\cos 45})^2 \\ 2=1+1 \end{gathered}[/tex]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
