This song came on the radio this morning, which naturally made me think of trig (less the song, more the band - sorry if I was ambiguous). I thought that if I was teaching the ambiguous case I would start with an activity like this.
Student would be paired up and one of each pair (let's call this student A) would receive an envelope. Their job would be to describe the contents of the envelope to student B so that student B could replicate it. Student B could not ask any questions, nor could they show their work until they finished. Then the two students would compare triangles.
Inside the envelope would be something like this:
I would be curious to see how many students would create a triangle that matched.
The irony here is that I don't teach the ambiguous case. I teach trig before it and trig after it, but not that part!