# Sine LAW

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Joined: Jan 8 2013 - 10:45am
Points: 3984
Sine LAW

Sir I was just wondering about the application of sine law.
does it apply when the largest angle is unknown?
i dont know where i got wrong. can you pls review my solution in the attached image below.
Im wondering why is it when alpha is unknown i arrive to the correct angle
and when i let the gamma as unknown, i get 75degrees instead of 104degrees.
i know had mistake in calculation but i dont know where..... ???????

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Joined: Oct 12 2008 - 3:39pm
Points: 1837
Re: Sine LAW

Arcsine will always return an acute angle. Example, sin-1 (sin (150°)) = 30° when we expect the calculator to return 150°. I made this a rule of thumb; if I am not sure that the angle is acute or obtuse, I do not use sine law. I use cosine law instead. Arccosine will always return the exact angle no matter if it is obtuse or acute. Example, cos-1 (cos (150°)) = 150° as we expected.

With the problem you posted, since we know that δ is obtuse because the sum of α and β is less than 90°, we can take δ equal to 180° minus the calculator answer from sine law. You can always do that if you are sure the angle is obtuse and not acute. 180° - 75.96° = 404.04°.

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Joined: Jan 8 2013 - 10:45am
Points: 3984
Re: Sine LAW

thank you very much! now i got it. btw 180° - 75.96° = 104.04°

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Joined: Oct 12 2008 - 3:39pm
Points: 1837
Re: Sine LAW

Yes, hahaha... It is 104.04°, thanks.

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Joined: Mar 4 2013 - 3:30pm
Points: 15
Re: Sine LAW

The Sine Law was not meant for this situation. Use the Cosine law to avoid any problems. When you have the 3 sides, to find angles, the Cosine Law is the golden rule.
If side a is the opposite to angle A:
a^2=b^2+c^2-2bcCos(A).
Cos(A)=(b^2+c^2-a^2)/(2bc). Always good.
Ok!

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