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# Sine rule or cosine rule? watch

1. Say I have two sides, one angle, and I do the sine rule to look for possible values of another angle, of which I also know its side - cool.

Then I am asked to find the possible angles and side lengths of the third side. I can figure out the angle of this side by 180-(known angle + possible value of other angle) and then doing that again for the other possible value. However, do I then do the sine or the cosine rule to find the length of this third side? I've found that using either produces different lengths, which is not what I would expect.

Any help?
2. (Original post by BestProfileName)
Say I have two sides, one angle, and I do the sine rule to look for possible values of another angle, of which I also know its side - cool.

Then I am asked to find the possible angles and side lengths of the third side. I can figure out the angle of this side by 180-(known angle + possible value of other angle) and then doing that again for the other possible value. However, do I then do the sine or the cosine rule to find the length of this third side? I've found that using either produces different lengths, which is not what I would expect.

Any help?
Using the sine rule or cosine rule should give you the same answer. You must have made a mistake in your working.

Can you post your question and working?
3. (Original post by BestProfileName)
Say I have two sides, one angle, and I do the sine rule to look for possible values of another angle, of which I also know its side - cool.

Then I am asked to find the possible angles and side lengths of the third side. I can figure out the angle of this side by 180-(known angle + possible value of other angle) and then doing that again for the other possible value. However, do I then do the sine or the cosine rule to find the length of this third side? I've found that using either produces different lengths, which is not what I would expect.

Any help?
Perhaps you could give the actual question since you can, indeed, use either
4. (Original post by notnek)
Using the sine rule or cosine rule should give you the same answer. You must have made a mistake in your working.

Can you post your question and working?
Sure:

a=11 c=4 C= 10degrees

So I used the sine rule to find that A could be 28.5 or 151.5.

"Find possible values for the remaining angle B and the correspondinglengths of the remaining side b, giving your answers to one decimal
place."

So here I did the sine rule like this:
a/SinA=b/SinB
11/Sin28.5=b/Sin141.5
b=11xsin141.5/sin28.5
b=14.4

But with the cosine rule:
b^2=a^2+c^2-2acxcosB
b^2=11^2+4^2-2(11)(4)xcos(141.5)
b=sqrt(205.869 etc)
b=14.348

If I do that for the other possible values the sine rule gives me 7.312 and cosine gives me 7.317 - not enough to mess that one up. I wonder if it is an issue of me having to do further decimal places because 28.5 etc is because the first part told me to only do it to one decimal place.

Thanks.
5. (Original post by BestProfileName)
Sure:

a=11 c=4 C= 10degrees

So I used the sine rule to find that A could be 28.5 or 151.5.

"Find possible values for the remaining angle B and the correspondinglengths of the remaining side b, giving your answers to one decimal
place."

So here I did the sine rule like this:
a/SinA=b/SinB
11/Sin28.5=b/Sin141.5
b=11xsin141.5/sin28.5
b=14.4

But with the cosine rule:
b^2=a^2+c^2-2acxcosB
b^2=11^2+4^2-2(11)(4)xcos(141.5)
b=sqrt(205.869 etc)
b=14.348

If I do that for the other possible values the sine rule gives me 7.312 and cosine gives me 7.317 - not enough to mess that one up. I wonder if it is an issue of me having to do further decimal places because 28.5 etc is because the first part told me to only do it to one decimal place.

Thanks.
Those are the same answer ... It is just the decimal place of the 28.5 etc as you say

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