Sine is opposite/hypotenuse. Opposite of angle S is line QR, which is unknown. Therefore start with the Pythagorean Theorem to find QR. For simplicity, I'll use x as a variable for QR.
\(x^{2}\)+60²=68²
\(x^{2}\)=68²-60²
\(x^{2}\)=4264-3600
\(x^{2}\)=1024
x=\(\sqrt{1024}\)
x=32
So QR is 32. Therefore, sin S is 32/68, which simplifies to 8/17.
