What three ratios of the lengths of two segments equal?

Since sin is opposite/hypotenuse, it can be a/(r+s) since r+s (aka e) is the biggest length in the bigger triangle, h/b since b is the hypotenuse in the right triangle, and the third one is tough - since the triangle with BC as the hypotenuse is similar to the biggest triangle (since e is parallel to s), the angle is either equal to B or C. Since angles B clearly are the same in the biggest triangle and the smallest, that's not possible, so it's angle C. The opposite/adjacent of that is s/a - I challenge you to use this technique for C and D!