So can i use the sine rule to find DC?

We don't know the length of AB and AC, sine rule can't be used...

But i find the angle DAC first. Then i use h/sin(pi/4)+x=DC/sin (pi/4)+x to find DC. Can it be accepted?

I know your mistakes now :
1) the x is part of the angle, it cannot be put outside of the sine, sin(pi/4 +x) should be the right way to write
2) the remaining angle DAC is pi/2 - (pi/4 + x) = pi/4 - x, the way you write is wrong

You can use sine rule in this case, then use sin(A+/-B) expansion to expand sin(pi/4+x) and sin(pi/4-x)...

I expand already and i use the small angle approximation, but i can't still work out the working

I attached another photo, which uses your sine rule, it goes back to the same working, you check the photo...
Or you attached your working, I check your working...