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.
[tex] x^{2} [/tex]+60²=68²
[tex] x^{2} [/tex]=68²-60²
[tex] x^{2} [/tex]=4264-3600
[tex] x^{2} [/tex]=1024
x=[tex] \sqrt{1024} [/tex]
x=32
So QR is 32. Therefore, sin S is 32/68, which simplifies to 8/17.
