Sine Rule: Ambiguous Case (1 Viewer)

[kpq_sniper017]

I left it till a bit late:

But how do you find out if the ambiguous case arises?

If you were to write down two solutions to a triangle, but there's actually only one, would you be marked down?

 

[Winston]

Originally posted by pcx_demolition017
I left it till a bit late:

But how do you find out if the ambiguous case arises?

If you were to write down two solutions to a triangle, but there's actually only one, would you be marked down?

Well i'm not sure what answer they take into account. But they might be lenient to give you a tick for the answer, take note your working out is an impact too. But i mean how can you have two answers? :S... that's if you don't know what you're really trying to find exactly and you provide both of the possibilties.

 

[CM_Tutor]

You can have two answers when there are two possible triangles. For example, consider a question like:

ABC is a triangle in which side AB is 10 cm long, and angle CAB is 20. Find the size of angle BCA if side BC is 8 cm long. There are two possible answers.

This problem - finding an angle using the sine rule - is one that all students should take care with. You must ALWAYS consider the possibility of two cases, as you can get the wrong answer if you don't - look at the Uluru problem from Q 7 of the (I think) 1994 3u HSC if you don't think this can come up. (Can someone please check I have the correct paper - I don't have my papers with me at the moment.)

 

[Xayma]

Of course it can come up, when dealing with one angle that could be obtuse or acute because sin x^o=sin (180-x)^o where 0<=x<=90

 

[kpq_sniper017]

OK.
Does that mean that as long as (180-x)^o gives a "valid" angle (i.e. when added to the other angle, does not exceed 180^o, and x^o is also a solution of the triangle, then there are two possible triangles?

 

[CM_Tutor]

Yes.

 

[kpq_sniper017]

Originally posted by CM_Tutor
Yes.

ok.