Ambiguous Case Law of Sines

Learn how to solve a triangle using the law of sines when it is the ambiguous SSA case in this free math video tutorial by Mario's Math Tutoring.
0:55 How to Drop an Altitude to Analyze the Triangle
1:07 Solving for the Height Using Sine
1:36 sSa Condition
2:13 Showing How the Side Opposite the Angle Can be Rotated
2:45 How to Know How Many Triangles are Possible
3:30 Splitting Up the Diagram Into 2 Possible Triangles and Solving
Related Videos:
Law of Sines
• Law of Sines (Trigonom...
Law of Cosines
• Law of Cosines
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[@MariosMathTutoring]

See more on this topic by watching this other video I did on the SSA ambiguous condition: kzbin.info/www/bejne/m53di4p7Z55qjcU

[@bard.zzzzzz]

this video was actually so concise and it helped me visualise and understand WHY there is an ambiguous case. thanks man

[@AndrewYatzkan]

but what's the main thing he wants to?

[@joebream5526]

Andrew depends on the question, most likely to find all angle measures and side lengths

[@alncrts4936]

The main thing he wants to do is

[@TooWongCool]

I've watched a bunch of different Law of Sines clips to help with studying, and you are the only one to bring up the isosceles triangle theorem. That theorem is what I needed a refresher on to understand which angle, on the case two triangle, gets subtracted from 180 to find correctly find all the case two triangles. Thanks!

[@MariosMathTutoring]

You’re welcome David! Glad my video was able to help you!

[@azurev2258]

You just taught me in five minutes what my math teacher failed to teach in three classes, huge help

[@AlexBaillie]

Thanks so much for this video! I have a test tomorrow, and this is the only good video on KZbin about this!

[@MariosMathTutoring]

+Alex Baillie great! I’m glad my video is helping you. Thanks for commenting. Good luck on your test!

[@AlexBaillie]

Thanks Mario!

[@abdurkhan6075]

same situation here and thnx

[@MariosMathTutoring]

Your welcome! Glad my video helped you!

[@filthycockatoo2954]

How did it go?

[@levirosner1728]

I've been really confused about the ambiguous case for so long and this really helped me understand how and why it is the way it is. Thank you so much!

[@enjoyablecheddar6882]

this is two years later but thank you so much for explaining it so easily. It was such an intuitive explanation and I understood it the first time. Thank you Mario!

[@MariosMathTutoring]

You’re welcome! Glad you liked my explanation!

[@Timapro_m10]

Say h

[@aryanruparel4257]

This is AMAZING. I literally watched video with animation before this, and they didn't know how to teach. This guys sticks to the whiteboard and is so good at teaching. Thanks so much!

[@mustafaassal]

I love you so much Mario. Ur a total legend. Thanks you

[@MariosMathTutoring]

Glad you like my videos and channel Mustafa!

[@omseif]

My son is having a unit test , and u r the best who explained this on you tube!👏👏 I'll make sure he watches this! I am sure he will be a fan from now on! Big Thanks!!!👍😊

[@MariosMathTutoring]

You’re welcome! Glad you liked the video!

[@ananyapal2458]

idk why MY math teacher overcomplicated this lesson and didn't just teach it like this! Never underestimate math videos from 5 years ago!!

[@xxPointedSalamander17]

I was really confused on this part of the precalc unit. You completely cleared it up for me. Thanks you so much sir.

[@MariosMathTutoring]

Happy to help

[@alaukip4130]

I love this video!! My math final for sophomore year is in 2 days and this really cleared up my confusion on this topic, thank you so much! I always go to your videos for math help. Keep making more videos, you're awesome!!👍🏼👍🏼

[@MariosMathTutoring]

Thanks Alauki! Good luck on your math final! Report back and let us all know how you did if you want. Glad my videos and channel are helping you!

[@filthycockatoo2954]

How did the math final go?

[@shenerhasan5421]

we're all waiting

[@alliep6999]

​@@MariosMathTutoring I am now in my sophomore year of COLLEGE! time flies!! it's hilarious to see people commenting on this still. I will say though that according to my transcript, I got an A in the class that year. Since then, I went on to complete the entire calculus series in my first year of college with great grades. Just goes to show that it's possible to progress even if you're struggling. keep doing what you're doing, you're appreciated!

[@alowrn]

@@alliep6999that’s amazing congrats!! how r u doing now

[@daniellin8088]

so grateful for people like you Mr. McLogan. thank you so much

[@chendusingh]

wrong channel lol

[@arielmutebi]

This is MUCH more clear and well-explained than my textbook. Thanks A LOT!

[@MariosMathTutoring]

Glad my video helped you understand the ambiguous case!

[@nazirulafif1857]

Thank you so much Mario. You really helped me a lot in Pre-Calculus.

[@provokingpickles1108]

Bruh this is so clutch, my math teacher explained this kinda weirdly but this makes so much sense. Thanks man 👍

[@MariosMathTutoring]

You’re welcome! Glad my video on the ambiguous case helped you understand it better.

[@provokingpickles1108]

Got a 93 on the test!!!! Thanks Mario 😎

[@bobbylook6076]

This really helps guy. If you are precalculus this will help you in ssa unit. Thank you for the video it help a lot.

[@benpoulos7015]

mans is life saver🙏🏽 made this so much easier to understand. thank you so much

[@adiliraliyev5882]

Thx, helped me alot, was breaking my head over how can you have 2 triangles with same h

[@picaa]

explained it better then Brian McLogan

[@Icemocha27]

Thanks a million for explaining this step-by-step!!!!

[@katiegriffith9935]

Thank you so much! This was so clear and helpful!!

[@MariosMathTutoring]

You’re welcome Katie! Glad my video helped you!

[@Sarsahhh]

I always come back to this video!

[@MariosMathTutoring]

Glad this video has been helpful for you.

[@turtles38x19]

damn...huge epiphany / mind blown when you drew that circle thanks!!!

[@mitchlaber7723]

Try Trisolve

[@rileydevitt7596]

Thank you so much for the help in this subject!!!! It makes a lot more sense now

[@MariosMathTutoring]

You’re welcome!

[@ellaveysel1041]

Ah! Math midterm tomorrow and this is going to save me!

[@MariosMathTutoring]

Glad my ambiguous case for the law of sines video is helping you Ella!

[@ruirui4087]

THANK YOU SO MUCH!!!!!!!!!

[@SharonKemboi-m1o]

thank you so much this was an excellent video really help me for my test

[@MariosMathTutoring]

You’re welcome! I’m happy to hear that my video helped you.

[@aidenackerman3657]

So for a 2 triangle case the other ambiguous angle would need to be greater than the give angle in one case and leave enough room for the given angle in another case?

[@TrazBurger]

Math final tomorrow, thank you so much

[@yipyiphooray339]

Helllooooo I loveee your video, I can see why my teacher told us to watch this. I'm still curious as to what the main thing u wanted us to know though 😆

[@lionelpham7232]

Mario the GOAT

[@merutshankar1158]

Bless you and your family. Thank you so much for this

[@MariosMathTutoring]

You’re welcome Merut! Glad my video helped you!

[@nico-rd6lp]

this is amazing thank you

[@andrearueda2062]

cannot thank you enough for this!

[@vihanv8582]

Thank You SO Much! This method is so much easier than other methods! I have a test coming up and this video helped me alot!

[@MariosMathTutoring]

Your welcome! Glad my video was able to help you. Good luck on your test!

[@yashb2997]

Thanks a lot for such a great video!

[@jamesberry8198]

Thank you! I am supposed to teach this in 5 hours and haven't done it myself since 8th grade haha

[@liviousgameplay1755]

"If you are describing the angle first then the two sides, why not write it from left to right?" *Writes the condition form left to right* "Oh. Nevermind." Banter aside, great video. I understand this much better now!

[@JohnBrown-dx8kp]

actually a lifesaver. guess like I'm not failing math this semester!

[@MariosMathTutoring]

Glad my video helped you John!

[@justchloe4753]

Thank you so much for this video, I actually understand ambiguous triangles now lol

[@MariosMathTutoring]

Glad you liked my ambiguous triangle video Chloe!

[@hojosa4592]

hi sir great video quick question could we also use the cosine rule to work out missing lengths for this case as we have cos(30) and values for a and b?

[@beedlejeedle]

Thank you so much! Just learned this today and I have a quiz tomorrow, you're a life saver

[@MariosMathTutoring]

You’re welcome Carol! Good luck on your quiz! Report back if you want and let us all know how you did.

[@SW-nx4jz]

This video was so helpful omg! Thnx you!!!!

[@MariosMathTutoring]

Glad my video helped you!

[@findo9615]

Woah. That makes a lot of sense. I gotta big unit test tommorow, thanks for this.

[@MariosMathTutoring]

+Fin Do your welcome! Good luck on your test!

[@hongningsuen1348]

A complete explanation of ambiguous SSA should include obtuse angle A. For acute angle A, SSA is not ambiguous congruence test when A is a right angle (actually the congruence test RHS) and when side S opposite angle A is the longer side (true for obtuse angle A as well) leading to one valid acute angle answer (angle of sine function in quadrant I) and one invalid obtuse angle answer (angle of same sine function in quadrant II). The invalid obtuse angle actually is in a triangle formed by the two given S's and an opposite extension of the third side. Hence SSA is not always ambiguous and is perfectly a valid congruence test when A is a right angle or S opposite to A is the longer side.

[@benjaminhoang5757]

amazing vid dude

[@MariosMathTutoring]

Glad you liked the video Benjamin!

[@samdarnold3563]

Hi Mario. Just a quick question. If the side b is equal to side a, is there 1 or 2 triangles?

[@MariosMathTutoring]

If I understand you correctly Sam and you are given SSA and the two sides are the same then the triangle would be isosceles and there would be just one triangle possible.

[@samdarnold3563]

@@MariosMathTutoring Thank you! You understood exactly what I was asking. I really enjoy your videos and I'll share you channel with all my classmates.

[@syntaxerror831]

Thank you for your very well done video explaining this topic in such an understandable way. Learning has proven tricky during this COVID-19 pandemic and this video truly has helped fill some gaps.

[@MariosMathTutoring]

Glad my video helped you!

[@matthew8780]

Very helpful, thank you

[@sweetstuff636]

This was very helpful thank you!!

[@MariosMathTutoring]

Your welcome Nicole! Glad it helped!

[@vincecastillo4962]

1:55 is the important part in my opinion

[@Fadic4]

thank you so much this helped a lotttttt

[@MariosMathTutoring]

+Fadic 4 your welcome. Glad my video helped you.

[@Fadic4]

if they give you b = 22, c = 32, B = 26° how do you know how many solutions you have because i cant figure out the height if i were to draw a perpendicular line

[@MariosMathTutoring]

+Fadic 4 draw the altitude(and find its length) from vertex A perpendicular to side BC then analyze the number of solutions from there.

[@cejuvlogs9766]

"But without faith it is impossible to please him : for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him." Hebrews 11:6 KJV

[@sarahle7160]

Why does the second triangle have the same side as the big triange ?

[@nathan2035]

Why do we need to solve for height though?

[@MariosMathTutoring]

It’s to help you determine the number of triangles that can be made.

[@nathan2035]

@@MariosMathTutoring Oh okay thank you! By the way your videos are great keep it up!

[@MariosMathTutoring]

Thanks Nathan! Glad you are liking my videos...new videos released weekly...so more are on the way...

[@Gcoff4]

Tricky topic, but good video

[@MariosMathTutoring]

Glad you liked the video!

[@mateosabio2857]

THANK YOU !!!!

[@MariosMathTutoring]

You’re welcome Mateo!

[@aris.barsekhian]

Thank you so much.

[@MariosMathTutoring]

+Aris Barsekhian your welcome

[@Fire_Rice]

wow youre so smart and a good teacher! take my babies

[@dr.stevephil6700]

das prty dope thunks

[@arishali5975]

thank you so much!!!!!!!!!!!!!!

[@MariosMathTutoring]

Your welcome! Glad my video helped you!

[@edsonlima6412]

Thanks a lot.

[@MariosMathTutoring]

Your welcome Edson!

[@vedpatel8365]

😃

[@pakchannel2231]

Thank youuu!

[@MariosMathTutoring]

You’re welcome! Glad my video helped you!

[@wendymarshall2132]

Thanks!

[@MariosMathTutoring]

+Wendy Marshall your welcome

[@hamidgul7224]

thanks!

[@MariosMathTutoring]

You’re welcome Hamid!

[@bambiii787]

So if you don’t have two triangles then you can’t do it?

[@NoelRandom]

bruh i still dont get it

[@mikebarlow3253]

I’m confused how a triangle could be 1 triangle 2 triangles or none. How can a triangle be more than one triangle?

[@MariosMathTutoring]

Since the information given about the triangle is limited it could possibly be constructed in more than one way or may not be possible at all…that is what this video shows….

[@azizkash286]

Legend

[@MariosMathTutoring]

Thanks Aziz! Glad you like my videos and channel!

[@michaelwilmarth7816]

damn the noise that marker made when he first twisted the cap off.... u know that mug a virgin

[@mattye3173]

So....3 and a half years later, what is the main thing he wants us to know?

[@MariosMathTutoring]

Sorry I don’t understand your question Matt...?

[@mattye3173]

@@MariosMathTutoring at the end, there was a cutoff

[@potatotree7143]

:) thanks

[@MariosMathTutoring]

You're welcome!

[@railgunawesome7114]

To the 35 people who disliked: why? You came for ambiguous law of sines, you got ambiguous law of sines

[@jaywankhede3426]

Alright 4 years later does he reply....

[@lindariestra9413]

MY MESSIAH

[@simpleman283]

👍👍

[@___xyz___]

5:10

[@enigmanightforce791]

Took you 5 minutes to explain clearly what my teacher spent 90 minutes explaining weirdly 🤦‍♂️ 😂

[@thecontrabandcap]

My trig teacher kinda sucks, this slaps

[@Nora-ks2sq]

I am so fucking confused.

[@adefela]

Thank you very much!

[@vincentha7123]

thank you so much!

[@Msbeatricemay]

Thank you!

[@MariosMathTutoring]

You’re welcome Beatrice!

[@dr.derplols8312]

Thank you so much!