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How to determine if you have 0,1 or 2 triangles for the ambiguous case

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How to determine if you have 0,1 or 2 triangles for the ambiguous case

287,788 views October 26, 2016 3:05

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ChannelBrian McLogan

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👉 Learn how to determine if a given SSA triangle has 1, 2 or no possible triangles. Given two adjacent side lengths and an angle opposite one of them (SSA or ASS), then there are 3 possible cases: there can be 1 solution, 2 solutions, and no solution.

Using the law of sines, we can obtain the value of the angle opposite the second given side length.
Case 1: If the product of the sine of the given angle and the given side adjacent to the given angle is greater than the given side opposite the given angle, then there is no possible solution satisfying the given values.
Case 2: If the obtained angle is greater than the given angle, then there are 2 possible solutions satisfying the given values.
Case 3: If the obtained angle is less than the given angle, then there is only 1 possible solution satisfying the given values.

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Organized Videos:
✅ Law of Sines
youtube.com/playlist?list=PL0G-Nd0V5ZMoSv8cypcR…
✅ Determine 1, 2 or No Triangle
youtube.com/playlist?list=PL0G-Nd0V5ZMpHLqyVTeo…
✅ Law of Sines | Learn About
youtube.com/playlist?list=PL0G-Nd0V5ZMoKvxj3KTY…
✅ Law of Sines | ASA
youtube.com/playlist?list=PL0G-Nd0V5ZMp0Wkn3bvl…
✅ Law of Sines | AAS
youtube.com/playlist?list=PL0G-Nd0V5ZMoMYbsUKx8…
✅ Law of Sines Ambiguous Case 2 Triangles
youtube.com/playlist?list=PL0G-Nd0V5ZMo8MMldMYz…
✅ Law of Sines Ambiguous Case 1 Triangle
youtube.com/playlist?list=PL0G-Nd0V5ZMoewwFmBZI…
✅ Law of Sines Ambiguous Case No Triangle
youtube.com/playlist?list=PL0G-Nd0V5ZMqAWofxWk7…
✅ Ambiguous Case Law of Sines | Learn About
youtube.com/playlist?list=PL0G-Nd0V5ZMq98rh3vv1…
✅ Find the Area of an Oblique Triangle SAS
youtube.com/playlist?list=PL0G-Nd0V5ZMopITRA5z0…

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👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: freemathvideos.com/about-me/

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About this tutorial

Brian McLogan published this 3:05 video tutorial on October 26, 2016. It has been watched 287,788 times on YouTube.

Category
Education
Duration
3:05
Published
October 26, 2016
Views
287,788
Likes
2,066

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Further reading

  • The Ambiguous Case of the Law of Sines Explained blog.cambridgecoaching.com

    By now, you know that you can use a combination of sides and angles to prove congruence between two triangles. For example, if you know the length of all sides, you can find all of the angles of that triangle. The side-…

  • The Ambiguous Case of the Law of Sines - Softschools.com softschools.com

    When using the Law of Sines to find an unknown angle, you must watch out for the ambiguous case. This occurs when two different triangles could be created using the given information. For example, take a look at this pi…

  • Solving Oblique Triangles: The Ambiguous Case | SparkNotes sparknotes.com

    Figure %: Two sides of an oblique triangle and an angle opposite one of them are given, and the angle is obtuse. Summary of Ambiguous Case In the chart below, the ambiguous case is summarized. The given angle can be eit…

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