[math question] right angle triangle trig question

[Nikonnn]

I have a nice pic that would give the answer but cannot post any link

Anybody have a trick so i can post it

on flickr just add that after the ...com
/photos/nikonnnn

[Porcell]

@op I believe you should use 3 sig figures, because 2 is just part of the formula and the 16.0 is a measured quantity.
(for example if you were doing the area of a rectangle and the sides were 16.0 and 2, you would only use 1 significant number since they were both measured)

That's the "problem" I have with the teaching of sigfigs. One example could be a fenced area with 24 feet on one side and 6 feet on the other. Finding the area of this fenced area would be 144? But if "use significant figures" the answer is 100? If you are in school, and write "100" and expect to get a passing grade, you have another thing coming.

So significant figures are taught for the mere sake of teaching you sigfig, but in school-work it's mainly pointless. Furthermore, the INTENT of sigfigs is completely lost on the students. They don't know -WHY- you are supposed to do things a certain way, they just try and learn the rules about leading zeros and decimal points. Now if teachers actually taught in the context of what measurement error really is, maybe the students would do better.

What I'm getting at is that in the context of a math problem, numbers should be taken as a true value. If it says "What is 6 times 24" or even "The fence is 6 feet by 24 feet" you should take those measurements as true. It's only when you talk about measurement error that significant figures really have a place.

[Badpaladin]

Significant figures are taught often incorrectly, but they're incredibly important. Once you get into things where measurements are so precise that the act of measuring can change a system, not having a common ground on numbers is disastrous.

[bals]

That's the "problem" I have with the teaching of sigfigs. One example could be a fenced area with 24 feet on one side and 6 feet on the other. Finding the area of this fenced area would be 144? But if "use significant figures" the answer is 100? If you are in school, and write "100" and expect to get a passing grade, you have another thing coming.

So significant figures are taught for the mere sake of teaching you sigfig, but in school-work it's mainly pointless. Furthermore, the INTENT of sigfigs is completely lost on the students. They don't know -WHY- you are supposed to do things a certain way, they just try and learn the rules about leading zeros and decimal points. Now if teachers actually taught in the context of what measurement error really is, maybe the students would do better.

What I'm getting at is that in the context of a math problem, numbers should be taken as a true value. If it says "What is 6 times 24" or even "The fence is 6 feet by 24 feet" you should take those measurements as true. It's only when you talk about measurement error that significant figures really have a place.

I agree.
I think what you said is one of the reasons I didn't really understand sigfigs back in the day when it was being taught to us. We learned it in Chemistry so there was some place for it but then later in the day you go to a math class where you (likely) shouldn't use sigfigs unless the teacher specifically tells you to, they'll just tell you to round to 1 or 2 decimal points or something

[Dendrek]

That's the "problem" I have with the teaching of sigfigs. One example could be a fenced area with 24 feet on one side and 6 feet on the other. Finding the area of this fenced area would be 144? But if "use significant figures" the answer is 100? If you are in school, and write "100" and expect to get a passing grade, you have another thing coming.

So significant figures are taught for the mere sake of teaching you sigfig, but in school-work it's mainly pointless. Furthermore, the INTENT of sigfigs is completely lost on the students. They don't know -WHY- you are supposed to do things a certain way, they just try and learn the rules about leading zeros and decimal points. Now if teachers actually taught in the context of what measurement error really is, maybe the students would do better.

What I'm getting at is that in the context of a math problem, numbers should be taken as a true value. If it says "What is 6 times 24" or even "The fence is 6 feet by 24 feet" you should take those measurements as true. It's only when you talk about measurement error that significant figures really have a place.

There are two types of mathematical study: theoretical and practical.

Most math you learn up to 12th grade is theoretical. It's based on how the math "works" in a perfect setting. Often times, those "perfect settings" ignore dozens or more relevant variables. And the reason for this is because trying to add those variables would be way too complex to be learning at the same time. So instead, they teach you the most basic layer first. The next year (or lesson) they add on another layer of difficulty -- although often they don't even add on that new layer to the old; instead they teach the two separately. And once you've reached a high enough level of understanding, they begin to combine everything and even to toss in real-world conditions. It's at this point you begin to learn practical math. And it's sometime near this point that you should be learning about significant figures. Not before.