Ambigious case of the sine rule

[GGWP VCAA]

Hello hard workers!!!

Upon starting equilibrium in particles, we were taught how to use Lami's theorem and drawing ''triangles'' of forces. While i was doing this one question, i was trying to find an angle between forces, and it turns out that there were 2 different angles.......

I was not happy.....

Anyways could anyone tell me if we require the knowledge of the ambigious case of the sine rule for the exam?

TIA

[keltingmeith]

Hello hard workers!!!

Upon starting equilibrium in particles, we were taught how to use Lami's theorem and drawing ''triangles'' of forces. While i was doing this one question, i was trying to find an angle between forces, and it turns out that there were 2 different angles.......

I was not happy.....

Anyways could anyone tell me if we require the knowledge of the ambigious case of the sine rule for the exam?

TIA

Yes.

Just make sure to keep track of the angles/lengths and do bullshit checks so that you know you have right answers.

[lzxnl]

Ambiguous case of the sine rule comes in when you have sin a / A = sin b / B -> sin a = A/B * sin b and you're solving for a, which can either be arcsin(A/B * sin b) or pi - arcsin(A/B * sin b). One of these is obtuse (if not, both of these are identically pi/2). Look at your triangle and see if you are looking for an obtuse angle.

[GGWP VCAA]

Ambiguous case of the sine rule comes in when you have sin a / A = sin b / B -> sin a = A/B * sin b and you're solving for a, which can either be arcsin(A/B * sin b) or pi - arcsin(A/B * sin b). One of these is obtuse (if not, both of these are identically pi/2). Look at your triangle and see if you are looking for an obtuse angle.

so we look for the acute angle then or the obtuse angle?

[lzxnl]

Depends on what you see from the diagram.