How do we know were to round to on the degrees and lengths?
Know: I looked in the back but it had some rounded to different places.
Need: Will you give us a specific place to round to on a test or what?
The rule of thumb on rounding is 3 significant figures.
However this depends on the number of significant figures in your given information.
If an angle is given to the nearest degree, for example 39 degrees, then there are only two significant figures in your information and you generally expect your answers to be good to no more than two significant figures. This isn't a hard and fast rule, but it's not a bad rule of thumb at this point.
If your angle is good to 3 significant figures, as in for example 48.2 degrees, then you expect an answer to be good to no more than 3 significant figures. Again, not a hard and fast rule, but not bad.
Mathematics texts can be pretty vague about significant figures. For example if the side of a triangle is 70, does that mean the the number is rounded to the nearest 10 units, that it's good to the nearest unit, or maybe even that 70 is taken to be exact.
Textbooks aren't even consistent in their treatment of these questions, and to be honest I'm not sure what level of rigor our text (with which I wasn't familiar before this term) uses for significant figures. I'll take a look at the text and address this question further in class.