Answer:
[tex]BC=6\sqrt{2}\ units[/tex]
Step-by-step explanation:
In this problem i will assume that the side AB is the hypotenuse
The picture in the attached figure
we know that
In a right triangle, if one angle is 45 degrees, then the other angle complementary is equal to 45 degrees too
so
[tex]m\angle B=45^o[/tex]
In the right triangle ABC
[tex]cos(B)=\frac{BC}{AB}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
we have
[tex]cos(45^o)=\frac{\sqrt{2}}{2}[/tex]
[tex]AB=12\ units[/tex]
substitute
[tex]BC=cos(B)(AB)[/tex]
[tex]BC=\frac{\sqrt{2}}{2}(12)=6\sqrt{2}\ units[/tex]
