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

👉 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.

Organized Videos:
✅ Law of Sines
✅ Determine 1, 2 or No Triangle
✅ Law of Sines | Learn About
✅ Law of Sines | ASA
✅ Law of Sines | AAS
✅ Law of Sines Ambiguous Case 2 Triangles
✅ Law of Sines Ambiguous Case 1 Triangle
✅ Law of Sines Ambiguous Case No Triangle
✅ Ambiguous Case Law of Sines | Learn About
✅ Find the Area of an Oblique Triangle SAS

Connect with me:

#analytictrig #brianmlogan

[CryptoSlice]

"Case 2: If the obtained angle is greater than the given angle, then there are 2 possible solutions satisfying the given values." This was all I needed to know for my final. Thanks Brian. You just have no idea how much you've helped me in this last year.

[daltonbrooks]

I really wish my teacher taught like you, her videos are so confusing. she makes Algebra 2H harder than it seems.

[sauce_servitor]

Just wanted to thank you again for all your help this semester. In pre calc, with my hard work and your videos, I managed to get an A! Thanks dude, your a legend

[curtismac]

Over half my class failed my math 20 last year, this is much more helpful then that teacher was

[FlameOfWar]

You've helped me so much, since you make videos that are super short and fast, it lets me watch like 10 of them to figure out why I have no triangles when there should be 2. Thanks so much!

[broch_evans]

Thank you so much for being dedicated to teaching and uploading! Your videos have been helping me learn and understand any confusing lessons now that I'm home schooled!

[jtrathbun]

Helped me so much in trig this year, thank you a ton

[zombbb]

i love this channel i have been struggling so much in class😭 thank you

[IfWeVibeWeVibe]

thank you so much u really bring back the classroom vibe🥺💜

[sarg]

But how do you know if the math you just did shows that it's truly a triangle and not something else

[trichad]

Is there 0, 1, or 2 solutions when both given sides are equal?

[mersadiesmiller]

you should title this how to find no solution in an ambiguous case... because thats all you showed here.. no help/:

[ginger_truncale]

Wow my teacher really could’ve just explained it this way and made it so much easier but no

[cl.]

How would you solve sin‐¹(any#) without a calculator? Because if it is a false domain, it doesn't really explain why and I want to specify

[hannahwillis]

please i have no tachers this year and i have no clue how to find sines or anything. im in geometry 1 and its kicking my butt dude it sucks i wish school could go back to normal id be doing so much better

[charlottemadden]

I’m in seventh grade and we’re doing this, but I have no idea what terms you’re using. Are there any simpler ways to find out how many triangles you can create with a certain set of dimensions? This video was definitely helpful, but I’m still confused.

[samiyahh]

Great video! Really helped!! Quick question: how can you tell if you have just one triangle or two triangles?

[gabriellamandebvu]

So we are to assume that the angle at B is 90 degrees?

[llamas]

my teacher said it was sinB/b= sinC/c he did c/sinC= b/SinB, is it the same?

[willcoomans]

how do you know when there are 2 possible triangles?