TIE - The Ambiguous Case Lesson

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The Ambiguous Case

In the previous lesson, you used Law of Sines, but only when given certain pieces of information about the triangles.

So far, you've used Law of Sines when you know two angles and any side. You can also use Law of Sines when given two sides and an angle not between (SSA). However, you must consider the possibility that there could be two unique triangles.

In the image below, imagine that you know sides a, b, and angle A. If you consider "swinging" side a, you can see how two different triangles could be created.

image of triangle ABC with sides abc with a "swinging" side a

Watch this video to learn how to identify and solve this type of triangle.

 

When you are given two sides and a non-included angle, you must consider the Ambiguous Case. You will not always have two triangles as in the previous video.  Sometimes you will be able to find just one triangle or sometimes, no triangle is possible.  This is why it is called the Ambiguous Case. Watch the video below to see different types of examples.

 

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