Because the sine of angles between 0º and 180º is cyclical, in some occasions when calculating an angle of a non-right triangle using the sine law it is possible to produce two different solutions.
The title of the grade 11 trigonometry lesson, “The Ambiguous Case of the Sine Law,” has always struck me as the possible title of a less than interesting Hardy Boys book. I mention this in class and inquire if any of my students is interested in producing an image to that effect. This spring one student, Ben, did! So I commissioned art from him and I am quite happy with the result. I quite like the graphing calculator. It sits proudly in my classroom.
I think this is his inspiring image:
