Ambiguous Case Triangle Math

Then if ab the side adjacent to the equal angles is less than or equal to bc so that de is also less than or equal to ef then the two triangles are congruent. An interesting problem arises when two sides and an angle opposite one of them are known. If angle a is acute and a h one possible triangle exists if angle a is acute and a h no such triangle exists.

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A unique triangle is not always determined.

Ambiguous case triangle math. The possible solutions depend on whether the given angle is acute or obtuse. For those of you who need a reminder the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles ssa. When the angle is acute five possible solutions exist. The ambiguous case often produces two possible completions of the triangle.

And c 6 in there are two different triangles that match this criteria. Consider triangles abc def. Side side angle is known as the ambiguous case. This is called the ambiguous case.

Let the angle at a be equal to the angle at d side ab equal to side de and side bc equal to side ef. In these two potential triangles the corresponding angles between the swinging sides and the unknown sides are supplementary. When using the law of sines to find an unknown angle you must watch out for the ambiguous case. If you are told that b 10 in.

For example take a look at this picture. This occurs when two different triangles could be created using the given information. When the angle is obtuse three possible solutions exist. As you can see in the picture either an acute triangle or an obtuse triangle could be created because side c could swing either in or out along the unknown side a.