Cake, when you first learned "sine" and "cosine" you should have learned that sine is "opposite side over hypotenuse" and cosine is "near side over hypotenuse". In problem one, you are told the length of the hypotenuse, 12 in, angle 35 degrees, and are asked to find (a), the side opposite the given angle: "opposite side over hypotenuse" is a/12= sin(35). You are also asked to find (b), the side near the angle: "near side over hypotenuse" is b/12= cos(35).
But, as Subhotosh Khan says, you do NOT "have to" use that. Once you know (a) you can use the Pythagorean theorem: \(\displaystyle a^2+ b^2= c^2\) where c= 12 and you have already found a: \(\displaystyle b^2= 12^2- a^2\), \(\displaystyle b= \sqrt{144- a^2}\).