SSA Investigation

dsark, Jan 24, 2014


  • 1. SSA, The Ambiguous Case for the Law of Sines
  • 2. Understanding The (Ambiguous) SSA Triangle Experiment

1.

SSA, The Ambiguous Case for the Law of Sines

A visual explanation of the ambiguous case for the Law of Sines given Side Side Angle (SSA).[br]Sides [math]a[/math] and [math]b[/math] and [math]∠A[/math] are given and can be changed by the user using the sliders or directly inputting values.[br]The student should start by increasing the length of side [math]a[/math], going through all 3 cases.[br]Then change all values at will to see the effects.
– Albert Navetta

2.

Understanding The (Ambiguous) SSA Triangle Experiment

To help you visualize the SSA (side-side-angle) triangle, consider the diagram shown below. There is no SSA congruence theorem for triangles because the number of triangles can change, depending on the relationship between the sides and angles provided, which is why it is called the Ambiguous case. There can be 0 triangles if the opposite side is too small. There can be 1 right triangle if the opposite side is equal to the height (Question: How do you calculate the height?). It can have 2 triangles if the opposite side is larger than the height. And, if the opposite side is too big (that is, bigger than or equal to the adjacent side), it will have only one triangle. Note: Hint to the question asked above: "How do you calculate the height?" The height can be calculated using the right triangle GAC.

Change the values of the three unknowns to help you develop a better understanding of the SSA triangle case.
– Shaffiq Welji

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