Law of Cosines

[@ldiazmdiaz]

I could picture you jumping when you are 80 years old. BAAM there goes AlGEbra.

[@profrobbob]

LOL...that's a great visual:) ...I hope I still have an audience to jump for...lol! Thanks for watching, I hope this means you are sharing my channel and that jumping with everyone!!!

[@Wubs4Scrubs]

Learned more in 15 minutes than I did during a 90 minute class period, thank you so much!

[@profrobbob]

5680pertive568 you're welcome!Please be sure to like, subscribe and spread the word if you continue to find this channel helpful:D

[@profrobbob]

You're welcome and thank you so much for supporting by subscribing! I hope you learned enough to go in and pass that trig exam with your new found knowledge!

[@orcfeseda]

The way you present the information is PERFECT! This has saved my behind on the upcoming tests and what not. Keep going please!

[@MikeyTwerpLj]

You are clearly going to be my math teacher for any more college math I need to do. You are like the BIGGEST life saver ever.

[@80beanz]

I have to say that as an older student in my 30's I have learned sooo much from the trig and pre calculus videos I supplement with what I am learning in college. Next stop calculus with profrobob. Thank you for the dedication and time you have put in to help make others interested in math. I tell everyone about your site :) Your a great teacher keep up the good work.

[@profrobbob]

You make a teacher proud:D...see that big smile on my face! And if you are still studying 9 hours later, I know your going to be ready to go into class and show your teacher who's been studying and who hasn't!!!

[@profrobbob]

Clint Eastwood couldn't have said it better.... Thank you for that glowing testimonial! I do love what I do and being a KZbin teacher in addition to a classroom teacher has taken it to a whole new level....especially after reading comments from loyal viewers like yourself! I really appreciate that you are sharing my site with others through your personal experience!..if I could only come up with a math video that would generate millions of views instantly:D

[@Ros2283]

You are the best! I can even skip class and still get an A in my Precal class thanks to your excellence in Pedagogy!

[@Antheraws]

Thank you so much for making videos I have found that as a student in college I really can't rely on my proff for teaching me the material thoroughly enough, so I am really glad that I have these videos to prepare for exams. Thank you so much you are a really good teacher.

[@mackenziecross2408]

You are seriously helping me majorly! I'm taking this course online and my grade at the end of the term determines if I get to go back to school or not. Up until now I thought I couldn't understand any of it and that I was doomed to fail! Now, I get everything you're saying and I feel like I grasp the concept. You are a great teacher!!!!

[@inanismailov]

You have no idea how happy i get when you jump in the video and will get the material in my head in 15 minutes.

[@profrobbob]

BAM!!! That's what I like to hear Inan Ismailov you keep studying and I'll keep jumping and making videos for you to learn from and share with all your friends & classmates:D Before you know it...the whole class will be shouting "BAM" when they get an answer correct:) lol

[@sundaydammy7507]

This is awesome! Explain better than my professor at school. Thank you so much sir! You just made my day... May God continue to bless you abundantly!

[@profrobbob]

Sunday Dammy thanks for choosing #ProfRobBob to watch, like, learn and sub to...keep spreading the word to help us groW and help others:D

[@GutierrezAnthony]

Honestly can't thank you enough for really breaking this down for me to fully comprehend, gonna ace this test in honor of you.

[@profrobbob]

You're welcome...and there would be no better compliment than that GutierrezAnthony ! Thanks for choosing #ProfRobBob to study with...BAM!!!

[@alexandrianc223]

I was absent when we covered this material and you just saved me from failing this quiz tomorrow. This is my new favorite channel to use when I need help with math!

[@profrobbob]

I am honored to be your teacher:) Please spread the word to help support my efforts. Slowly but surely I will be posting calculus videos through next year.

[@profrobbob]

Thank you Mackenzie...and you are an awesome student for not giving up and reaching out for some extra help! I hope my videos and your new found confidence continue to help you pass your on-line course with ease. I look forward to hearing the good news regarding your return to school...keep working hard and aim for that success thats right around the corner:)

[@starknakkid]

Your Trig videos are excellent. You are a great teacher, and it's a shame that more teachers could teach like you. Thanks for the vids.

[@profrobbob]

I approve all my comments to keep the channel suitable for all audiences and I just answered your first comment...I'm glad to see you are still watching more lessons and I hope you continue to find them helpful. I've had many viewers tell me they have started study groups and all watch a video and then together they work out problems...it always seems less dreadful if you have people to share with:)

[@Aryanne_v2]

The Law of Cosines and Sines confused me so much. Thank you for these. They explained them perfectly.

[@profrobbob]

You're welcome and thanks for watching and subbing! I hope you will tell your friends to watch and do the same:D

[@georgesadler7830]

Professor RobBob, thank you for a smooth introduction to the Law of Cosines. The Law of Sines and the Law of Cosines work side by side or together.

[@alexandrianc223]

I'm just letting you know that I got a 93% on my final exam in Honors PreCalculus!! Your videos really helped me and they're the main reason I got an A. Thank you so much and I'm definitely going to use your videos for AP Calculus next year!

[@MrSaintskid11]

Thanks So much... I would not have passed my test without this!

[@profrobbob]

You're welcome MrSaintskid11 thanks for choosing #ProfRobBob to sub to and study with...that's the way to make the grades count...BAM!!!

[@billyjames3258]

Thank you so much! I don't know what I was doing wrong but I was just not getting it. I watched a couple videos and looked up step-by-step solutions and yours is the only one that actually made sense! Thank you! :)

[@profrobbob]

You're welcome Billy James and thank you for not giving up and choosing my channel to learn from...BAM!!!

[@raejohnson2647]

Mr. T thank you so much for this video! I appreciate your excellent instruction and great teaching style. You're really a gifted teacher!

[@Som72829]

I learned so much more by watching your vids thank you so much!!!!!!!!

[@profrobbob]

+Andi Dittakavi you're welcome and thanks for choosing my channel to study with and sub to! Please spread the word:D

[@profrobbob]

You are so welcome! And thank you for subscribing and "liking" my video:) I grow through the support of happy subscribers spreading the word:D....BAM!...now go spread the word!!!!!

[@EP-rq3pn]

thank you, this was very helpful! After using LoC and then LoS to find the remaining angles, I couldn't figure out why one of my angles was 180 minus the correct answer. Yours was a clear explanation

[@profrobbob]

You're very welcome, glad I could help....thanks for watching and subbing too! Please share this channel with your teacher so ALL current and future students know where to find after school help...thanks in advance for your help and support...BAM!!!

[@kelvdawg]

you are the man. Without you, i would've definitely failed.

[@profrobbob]

BAM!!! Jedi thanks for learning with #ProfRobBob !

[@nilemajestylobusta667]

just have been doin' my 100-item assignment for almost 2 days, and when I've got your tutorial prof, so happy that i just have to download it and make it as my tutor.. thank you so much..

[@profrobbob]

You are so welcome nile majesty lobusta don't forget to like, subscribe and tell all your friends, classmates and teachers to watch and do the same:D Then the whole class will be able to "do their homework" ...lol

[@nilemajestylobusta667]

yes no problem prof.. i want to ask some tutorials again prof like inverse trigonometry and its applications.

[@DumbAndLethal]

During your 14 minute video, I learn an entire lesson. During a 1 hour lecture by my teacher, we cover a quarter of the material demanded in our homework if even that. Haha thanks for taking the time to make the videos.

[@profrobbob]

I am glad you found my video helpful. I don't have any football application videos ready...but I do wish you good luck on your project:)

[@profrobbob]

That is cool. I thought maybe you we looking for Cosine in Right Triangle Trigonometry. I just looked at the Geometry Honors book I am teaching from...new class for me this year...and I do see a small additional section that talks about Law of Sine and Law of Cosine. I am going to cover that so when my students have me in PreCalculus it won't be new to them:D I am glad you found my video helpful! Thanks for watching and please spread the word:)

[@School_Circle]

You are the reason I think I will pass my final tomorrow. Thank you keep working hard.

[@profrobbob]

You're welcome. By the time you are reading this I hope you went in and passed that final like BAM!!! Joshua Celis ! You certainly should for putting in so much study time and effort:)

[@vylon1092]

my college professor asked me to discuss law cosines in class, this video will really be a big help thanks

[@profrobbob]

Congrats on studying outside the classroom...I hope you will share my channel with your Professor and the rest of your class too:D

[@profrobbob]

BAM!...you're welcome:)....and thanks for "liking" my videos. I hope you will keep watching and learning and sharing!

[@profrobbob]

Thank you for subscribing as well!!! I really appreciate the support:)

[@profrobbob]

And THANK YOU for taking the time to watch them and comment! I hope this makes me your go-to channel for math help in the future:)...and it sounds as if others in your class might benefit from my channel as well, so please share and help me continue to groW!

[@vimboy10]

Hi Professor! :) I really appreciate your instructional video and it's more clearer to understand. :) And actually, on the spot, I quickly understand the lesson. Thank you so much for helping not only me but other students which are not good in Math. :) And actually now is just 1 hour before our quiz when I watched this. :)

[@profrobbob]

I hope you pass that quiz like BAM!!! Alecesse Vim Casinabe and thanks for choosing #ProfRobBob to watch and sub to and taking the time to "thank the teacher"! Please keep sharing my channel with others to help us keep growing:D

[@profrobbob]

You know it takes dedication from you to make that happen...I'm just here to furnish you with the lessons:) Keep up the great study habits and you'll change those 80's to 90's:) I just reminded you in another comment to keep sharing my channel with everyone:D Thanks for supporting!

[@alexandrianc223]

I can't remember if I commented back, but I owe you a lot of thanks because I studied for my Honors Pre-Calculus Final solely by watching your videos and I got a 93! So thank you!:)

[@profrobbob]

THANKS for subscribing and supporting!

[@Mikaila55123]

When you say SOHCAHTOA during the first 2 minutes i actually cry!! omg your to greatt! so helpful!!

[@profrobbob]

LOL...and THANKS for choosing Tarrou's Chalk Talk to watch and learn from Mikaila55123 ! Please spread the word and SUBSCRIBE to support and help my channel groW and help others:D

[@profrobbob]

Thanks for supporting my channel and liking my videos. I just try to make learning "FUN" while teaching at the same time:)

[@profrobbob]

Law of Cosines is now Closed Captioned:D

[@Asmrnerd10]

Professor Rob.When are we suppose to learn laws of sine and cosine?Also in what subject in math is this kind of formula more applicable?Thanks!

[@sanjeevradhakrishnan5871]

These concepts are typically covered in pre-calculus.

[@profrobbob]

I do that too sometimes. I am reposting a very long video to fix a mistake where I said 1+2 is 2, so it happens to all of us. I am glad I reminded you to check your calculator:)

[@profrobbob]

Thank you. Addition and Multiplication is commutative so I don't worry too much about exactly following the pattern of the formula. But, when doing an example I should have been a bit more careful about that:) Thank you and thank you for watching!

[@profrobbob]

Thank you for subscribing and I will try to continue my awesomeness:))

[@profrobbob]

Now that's what I call really "showing the love"!!! Thank you so much for your support and viewership:)

[@alexandrianc223]

I got a 94% on it! And thank you very, very much!! That means a lot!:) I'll definitely add you the the list:). And I thought you might want to know that instead of wasting my time going through my notes to study for my final tomorrow, I'm watching a bunch of your PreCalc videos and it's helping so much.

[@profrobbob]

Thank you very much:) I hope that means you will keep watching my other videos!!! :D

[@profrobbob]

Yes...the three interior angles of a triangle do add up to 180. I don't remember the exact example I did in this video and I can't watch it at this moment. It is not a bad idea to solve all the angles with either Law of Sine or Cosine just to check your work if you have the time. If one angle is given, you find the second with one of the Laws and just find the 3rd by subtracting from 180...you may be carrying through an error without knowing it to your next answer.

[@profrobbob]

Wonderful...now "BAM"...go get that A! And thanks for watching and sharing and supporting:)

[@NavyDude]

Good video. Helped a lot. I like how randomly energetic you became on certain things haha.

[@profrobbob]

You know you're a math geek when you get excited while doing math:) Thanks for supporting by watching and subscribing navy dude!…and thank you for serving our country:)

[@profrobbob]

You're welcome...and THANKS for watching too:)

[@profrobbob]

You're welcome...Thanks for choosing my channel to learn form:)

[@profrobbob]

Life-Vest provided at no charge...lol Thanks for choosing my channel to learn from!

[@miriamsoto2463]

Really great videos! I feel as if all I have to do is watch them and I'm completely prepared to take on my finals.

[@profrobbob]

I CAN be your teacher, 24hours a day even!...you have the power at your fingertips to click on my videos and learn anytime-day or night...LOL! I'm glad you found my channel helpful and thank you too for subscribing:) Please share with all your friends, fellow students and anyone who you want to share with:D Thanks for your support.

[@profrobbob]

Thanks for watching...I hope you will return whenever you need more math help in the future:)

[@profrobbob]

BAM!!! ...and "Thanks" for watching:)

[@rihuachen7834]

Thanks for adding in different scenarios like the bearings and whatnot. Great guide to review from!

[@profrobbob]

Thanks for choosing my channel to review from!

[@KeepingUp_withAI]

this is great, i had to miss class today so this more than made up for what i miss. Thank you!

[@coolrahul223516]

I have to be be honest that I do understand more from your videos than my class tutor

[@chriswilliams5291]

I was once told that a way to tell if a triangle is two or one triangles is if the two shorter sides squared is less than the longest side squared then it has two triangles. For example, in the problem in the video 5.5^2 + 6^2 = 66.25 which is greater than the longest side 7^2 so only one triangle.

[@profrobbob]

FANTASTIC! Thanks for watching:)

[@joew1865]

Thanks, Professor. Great lesson!

[@profrobbob]

You're welcome Joe W thanks for choosing #ProfRobBob to watch and sub:) Please tell everyone to like, share and subscribe to help my channel groW!

[@dinnerkill]

Thank you! Great teacher, always come to your videos help help. Keep doing what you do!

[@profrobbob]

You're welcome…nice to hear that you keep coming back when you need help:) I hope you will share my channel with your friends and don't forget to like and SUBSCRIBE to support!

[@profrobbob]

You are welcome:) Thanks for watching.

[@theBoiiiiiiiCReme]

you're awesome! You made understanding these topics easy!

[@profrobbob]

theBoiiiiiiiCReme thanks for watching and leaning from #ProfRobBob and please like, sub and share:D

[@MikeyTwerpLj]

The word is already spread :) Thanks again for taking the time to post these helpful videos.

[@profrobbob]

I am glad I can be here to help. Sorry to hear you don't feel like you are getting what you need from your teacher. I hope my videos can help you pass your class with flying colors. Please return the favor and pass on my math channel to anyone else you think it can help...and let me know how you are doing.

[@xXItstrayceceXx]

Thank you so much! I was so confused in math class untill I saw this video! I really appreciate it! :)

[@profrobbob]

And I appreciate you watching and learning from my videos! Don't forget to SUBSCRIBE and share with all your friends too:D

[@profrobbob]

No...this is a Pre-Calc video, from that library. You can search my channel page by subject, try that if thats not how you found this video:) Thanks for watching!

[@profrobbob]

The advertising supports my efforts as well as Google/KZbin, so there is definitely no sarcasm in my appreciation of the support of my viewers, subscribers, and supports:)

[@chriswilliams5291]

Thank you for the videos on the law of sines and the law of cosines I feel like, for the most part, I understand these concepts. The only thing I still somewhat struggle with is being able to tell if there are two solution triangles or only one. For example, in this problem, I would think there would be two solutions since 180 - 79.4 = 105.1 and 180 - 105.1 - 49 = 25.9 Is this not the case for the problem in the video, and if so why not?

[@profrobbob]

Because the information given is in the SSA pattern you want to watch my video Ambiguous Case Law of Sines. Thank you very much for watching.

[@profrobbob]

@xxSportsBoy17 AWESOME!!! I am thrilled to hear that you did so well:) Keep up the good work.

[@profrobbob]

What can I say...Math brings the geek out in me:)

[@rAdiOAcTiVepLum1]

Hey amazing video..i finally understood this concept...i was hoping if you could probably put a video up about its application in football..i have an assignment to do and it would really help

[@profrobbob]

You will find a video I think should help you in my video "applications of law of sines and cosines". You have to partially solve the oblique triangle defined by the two angles of depression and the mile distance between the markers before you can calculate the altitude of the balloon.

[@TANtrum30]

I love your energy and animation! lol

[@profrobbob]

Tanisha Williams THANKS for watching! I hope you will return to like, sub and share my channel with others:D

[@profrobbob]

If you are still watching and studying...take some time to stop the video and work out the example BEFORE I show it to self test yourself:) AWESOME job on the 94%! Let me know how you do on this next one too...just go in singing the answers and your sure to get an A. And I'll look forward to being a part of your "Check it Out" list...I promise to make you proud:D

[@edbertjaredatienza9373]

GOOD VIDEOS. Hope i could pass my exam with your help!

[@profrobbob]

Thanks for watching and subbing Jared atienza now go make me proud and pass that exam like BAM!!!

[@profrobbob]

Start the problem and find the angle opposite the largest side in case it is an obtuse angle. You would start with work like I am doing starting around minute 7:30.

[@darienperez-martin7783]

It would be awesome to see some applications. Off the top of my head I could think of how useful this would be to calculate the distance between various test charges and a source, and then us the results to calculate the strength of the electric force at that location in the electric field! Thank You!!

[@profrobbob]

I don't do any examples quite that involved but I do have this lesson. Applications of Law of Sines and Cosines

[@profrobbob]

That's awesome news! I'm glad you found my video so useful...let me know how you do on that quiz:) Thanks for supporting by subscribing too...maybe after you pass that quiz you'll even like my channel enough to add it to your :)Check Out list! My wife liked your "Lucky" video and says: keep singing...you have a great voice & with that big smile on your face and a song in your heart, you'll go far!

[@trieunguyen7530]

love your lesson keep it up. thank for the help

[@profrobbob]

You're welcome Trieu Nguyen ...thanks for choosing Tarrou's Chalk Talk to watch and subscribe to! You keep telling people about my channel and help me groW and I'll keep making videos...okay?!

[@juanignacio3305]

Another great video! Thanks!!

[@profrobbob]

***** :)

[@tkhagos]

question here...in the last example of this video, we're given two sides and one angle of a triangle, however after applying the law of cosine to find the the third side, can't we determine if the opposite angle of the largest side is obtuse or acute from the Pythagoras theorem and then we can straight head on to the law of sine to find the largest angle and then we take the supplementary angle instead by subtraction from 180°? while # 1 below is obvious, I'm not sure if # 2 and 3 will make any sense or if they're already established rules please excuse my slacking for not researching but right off my head I felt that, 1. right triangle, if c^2 = a^2 + b^2 2. if c^2 < a^2 + b^2, then the opposite angle of the largest side would be acute 3. if c^2 > a^2 + b^2, then the opposite angle of the largest side would be obtuse

[@profrobbob]

If you find it easier to check whether or not the angle is obtuse opposite the largest side, then go ahead:) Or, just don't use the Law of Sine to find the angle opposite the largest angle. You can use Law of Sine to find the measure of any of the other angles or Law of Cosine. I am emphasizing the use of Law of Cosine in this lesson because I am just introducing the Law of Cosine.

[@profrobbob]

I hope you do great on your test and thank you for the positive feedback:)

[@profrobbob]

Thanks for watching:)

[@UnleashMonkey]

great video, really helped!! small suggestion: maybe include a sample problem in the video description(with the answers all the way in the bottom) for viewers to try and test it out. by the way, I subbed. I'm sure I'll be on this channel a lot throughout the semester ^-^

[@profrobbob]

Thanks for watching, subbing and for the input. I do put more examples in my newer videos and most of my viewers tell me that they just hit the pause button and work the problem:) Hope you continue to find my videos helpful and take the time to spread the word and help us groW!

[@tylerbhame262]

you saved my grade thank you!

[@profrobbob]

+Tyler Bhame teamwork...you took the time to study, I furnished the lessons...BAM!!! Please like, sub and share if you continue to find these videos helpful:D

[@LilNicky109]

Amazing video!!! Thank you

[@profrobbob]

Thanks for watching...please sub and share too:D

[@profrobbob]

PS...THANK YOU for adding my channel to your :)CHECK OUT list as promised...I really do appreciate the support of loyal viewers like yourself!!!

[@JoshuaEchelon]

Do you have a video about Law of Tangents?

[@profrobbob]

Sorry...no I do not:(

[@alexandrianc223]

I've been doing that! And thanks hahaha I'll try that! As soon as I figure out how to edit the list I will add you:).

[@pimentejm]

Thanks a lot man I'm doing bad in geometry cuz of my confusing teacher but your videos are making up for it

[@profrobbob]

You're welcome...I'm happy I could supply you with the help you needed:) Thanks for watching and liking and I hope you will also take the time to share and SUBSCRIBE to continue to help my channel groW!!!

[@profrobbob]

Not all oblique triangles can be solved with Law of Cosine which is why we need Law of Sine as well:)