SSA triangle: The Ambiguous Case
- For finer control of the sliders, click the slider and use ←→ keys to adjust.
- Tab forward through input boxes and sliders, or shift-tab backward.
0 triangles In it's default state, the swinging side (labeled a by default) is not long enough to form a real triangle. For A < 90°, write an inequality in terms of given SSA parts (a, b, & A) that establishes when 0 triangles are formed. How about when A ≥ 90°?
1 triangle For A < 90°, drag the slider for side a until it is just long enough to form 1 triangle. What type of triangle is this? Write an equation in terms of given SSA parts (a, b, & A) that establishes when this 1 triangle is formed. As an alternative to using the slider in the GeoGebra construction, you may type such a trig expression into the input box for a. However, you'll need to enter numerical values in the input box instead of variables (e.g. 16 instead of b, 30° instead of A).
2 triangles For A < 90°, keep on lengthening side a until there are 2 possible triangles formed by the given info. This is known as the "ambiguous" SSA case because the given information doesn't specify which of the 2 triangles is desired for a particular situation. Keep on lengthening a until there are no longer two triangles anymore. Write a compound inequality in terms of given SSA parts (a, b, & A) that establishes when there are 2 triangles formed.
1 triangle For A < 90°, upon continuing to lengthen side a, at some point 1 of the 2 triangles becomes invalid and there is only 1 valid triangle left. Why did the 1 triangle become invalid? Write an inequality in terms of given SSA parts (a, b, & A) that establishes when only 1 valid triangle remains. How about when A ≥ 90°?