We have triangle ABC with the right angle (90 degree angle) at angle C. This is shown by the square marker. Another angle is given at angle A to be 40 degrees. We'll use the 40 degree angle as the reference angle.
With 40 degrees as the reference angle, we can apply the labels as you have done in the diagram. Nice job with that labeling so far.
hypotenuse (h) = side AB = 10
opposite leg (o) = side BC = unknown
adjacent leg (a) = side AC = unknown
I'm going to use "opp" for "opposite" instead of the letter o. Also I'm going to use "hyp" for "hypotenuse"
We want to find the length of BC, call it x for now, and we know the hypotenuse is 10. So we'll use the sine rule
sin(angle) = opp/hyp
sin(40) = BC/AB
sin(40) = x/10
10*sin(40) = x
x = 10*sin(40)
x = 6.427876 <--- use a calculator here
So side BC is approximately 6.427876 centimeters long
