Today in class we did a lot of things. We started with a warm up that asked us to find the triangle with these given sides and angle:
A=26º
a=5
b=8
This gave us an ASS (angle, side, side) case, which we know presents an ambiguous case. An ambiguous case provides you with information that you could use to create two different triangles. During this warm up we were asked to solve each angle and side of this triangle along with its area. Students could have solved for two different triangles with these given sides and angle. After the warm up we explored and proved the ambiguous case by constructing a visual of these possible triangles on Geogebra.

As you can see in the visuals there are two different triangles with values:
A=26º
a=5
b=8
This proves the ambiguous case.
We calculated the other possible sides and angles using the theorem that:




By Monday we are to prove that (when given SSS or SAS):



(and also find the largest angle when given SSS)

And for Bonus points we have the option to prove Heron's Area Formula (when given SSS) of:
, where s is the half perimeter.