Investigating the Ambiguous Case

Drag the sliders to adjust the length of the sides and , and the angle . Click the checkboxes to hide the height or the circle of radius centered at . Applet by John Chase.
Hide the "height." First, try making the angle an obtuse angle (greater than ). By adjusting the length of side , how many triangles can be formed? Next, try making the angle an acute angle (less than ). By adjusting the length of side , how many triangles can be formed?