Both have as their denominator the hypotenuse length.
1) Since we have a right triangle, and the missing leg is the hypotenuse. We can start by applying the Pythagorean Theorem to find out the hypotenuse:
[tex]\begin{gathered} a^{2}=b^{2}+c^{2} \\ a^{2}=3^{2}+4^{2} \\ a^{2}=9+16 \\ \sqrt{a}^{2}=\sqrt{25} \\ a=5 \end{gathered}[/tex]2) Since we have the length of the hypotenuse, let's focus on the sin(x) and cos(y)
[tex]\begin{gathered} \sin (x)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5} \\ \cos (y)=\frac{adjacent}{\text{hypotenuse}}=\frac{4}{5} \end{gathered}[/tex]We can memorize sin as SOH - Sine, Opposite, Hypotenuse, and forCosine = CAH= Cosine, Adjacent over Hypotenuse
3) Hence, both sin (x) and cos(y) have in their ratios the hypotenuse length as their denominator (bottom number) that's what they share.