Smallest angle of a triangle

Question

What is the smallest angle of a triangle with $area=40cm^2$ and one side $=12cm$?

I am stuck before i get started Please help me.

Answer 1

Imagine fixing the 12cm side of the triangle horizontally; call it the base. Now since the area of a triangle is determined by its base and height, the area condition fixes the height of the third point. We can still move the third point around horizontally without changing the base and area. What happens to the angles when we move that point around?

Answer 2

Altitude is $CO =6\frac23$, base is $AB=12$, $C$ goes to $\infty$ parallel to $AB,$ so that lines $ AC,BC $ coincide, is the limit solution narrow triangle of zero angle at vertex $C$ and area $ 40$.