Question

To solve a triangle (that is, find the lengths of all sides and the measures of all angles), we must have at least three of those parts. However, we can't just willy nilly pull three values out of thin air and expect to create a distinct triangle. For example, the three lengths 5, 8, and 14 cannot even form a triangle. Why? Seriously - why? Answer here. The Ambiguous Case of SSA When we are given three parts in the following arrangement, it might be that a triangle is not possible (no solution), or it might be that a single solution exists (a unique triangle), or it might be that there are two solutions (two triangles are possible). Because of this ambiguity, SSA is called the ambiguous case. this side given the side opposite the given angle is given this angle is given 1. Using a straight edge, draw to scale an angle and two sides in this arrangement that will not be able to form a triangle. Explain next to your drawing why a triangle is not possible (it should be obvious). 2. Sketch three sides in this arrangement in a way that will just be able to form a triangle. Using SohCahToa, how long will the side opposite the given angle be? 3. Reflect on what you've done so far. Make sketches with a single set of given information in this SSA arrangement showing not one but two different triangles. What is the criteria for a two-solution scenario?

          To solve a triangle (that is, find the lengths of all sides and the measures of all angles), we must have at least three of those parts. However, we can't just willy nilly pull three values out of thin air and expect to create a distinct triangle. For example, the three lengths 5, 8, and 14 cannot even form a triangle. Why? Seriously - why? Answer here.

The Ambiguous Case of SSA
When we are given three parts in the following arrangement, it might be that a triangle is not possible (no solution), or it might be that a single solution exists (a unique triangle), or it might be that there are two solutions (two triangles are possible). Because of this ambiguity, SSA is called the ambiguous case.

this side given
the side opposite the given angle is given
this angle is given

1. Using a straight edge, draw to scale an angle and two sides in this arrangement that will not be able to form a triangle. Explain next to your drawing why a triangle is not possible (it should be obvious).
2. Sketch three sides in this arrangement in a way that will just be able to form a triangle. Using SohCahToa, how long will the side opposite the given angle be?
3. Reflect on what you've done so far. Make sketches with a single set of given information in this SSA arrangement showing not one but two different triangles. What is the criteria for a two-solution scenario?

To solve a triangle (that is, find the lengths of all sides and the measures of all angles), we must have at least three of those parts. However, we can't just willy nilly pull three values out of thin air and expect to create a distinct triangle. For example, the three lengths 5, 8, and 14 cannot even form a triangle. Why? Seriously - why? Answer here.

The Ambiguous Case of SSA
When we are given three parts in the following arrangement, it might be that a triangle is not possible (no solution), or it might be that a single solution exists (a unique triangle), or it might be that there are two solutions (two triangles are possible). Because of this ambiguity, SSA is called the ambiguous case.

this side given
the side opposite the given angle is given
this angle is given

1. Using a straight edge, draw to scale an angle and two sides in this arrangement that will not be able to form a triangle. Explain next to your drawing why a triangle is not possible (it should be obvious).
2. Sketch three sides in this arrangement in a way that will just be able to form a triangle. Using SohCahToa, how long will the side opposite the given angle be?
3. Reflect on what you've done so far. Make sketches with a single set of given information in this SSA arrangement showing not one but two different triangles. What is the criteria for a two-solution scenario?

Added by Alfredo J.

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