@potatoeewedge
1. if m∠b = 32°, and ab = 12 cm, what is ac?
[see attachment]
(enter your numeric answer. round to the nearest hundredth.)
2. if m∠b = 41°, and ab = 5 cm, what is bc?
[same attachment]
(enter your numeric answer. round to the nearest hundredth.)
3. if m∠a = 56°, and bc = 24 cm, what is ac?
[same attachment]
(enter your numeric answer. round to the nearest hundredth.)

The given problem is a right triangle, we can use Pythagorean theorem and SOH CAH TOA in solving the unknown.
For item#1, 
sin B = AC/AB
sin 32° = AC/12
AC=6.36 cm

For item#2, 
cos B = BC/AB
cos 41° = BC/5
BC = 3.77 cm

For item#3,
tanA=BC/AC
tan 56 = 24/AC
AC = 16.19 cm

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.