How do i solve this using cosine or sine ratio?

You would use the simple format SOH-CAH-TOA
SOH: sine = opposite/hypotenuse
CAH: cosine = adjacent/hypotenuse
TOA: tangent = opposite/adjacent

So for this problem to find c you would use this equation: 
sin42= c/7
7sin42=c
c=4.68

Then for d you would use this equation:
tan48=d/4.68
4.68tan48=d
=5.197

Hope this helps :)