How to Use the Law of Sines in Trigonometry (Precalculus - Trigonometry 32)
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- Опубліковано 27 вер 2024
- What the Law of Sines is, When it works, and how to use it to find missing sides and angles in oblique triangles.
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I appreciate when you bring up stuff from the video before. Because I binge these videos and its so much information that if you don't mention again I will forget it because I'm going at such a fast pace.
Been loving all of your videos as Im going through trig. Really great job, Prof.
1:16:41 I thought I would add something interesting. I know this is a lesson on utilizing the Law of Sines, but I thought it would be nice to have another method available in the comments for anyone interested. Its using a system of equations instead of the Law of Sines:
You dont need to have any more angles than what is presented on the board. You are going to set up two equations and then solve them for an unknown variable and then put the two equations equal to each other. First to define some variables:
x = the unknown length listed as a (?) on the board
h = the height of the volcano
First equation:
tan(35) = h/(900 + x). See that this is just normal right triangle trig here. Tangent of the angle equaling the rise/run. The (900 + x) is the full length of a bigger right triangle that includes that 35° in the corner.
Second equation:
tan(45) = h/x. See that this is a smaller right triangle and that this is just normal right triangle trig here.
Solve both equations for "x" and then set them equal to each other:
(h/tan(47)) = (h/tan(35)) - 900
Move (h/tan(35) to the left and factor out the "h":
h [((1/tan(47)) - ((1/tan(35))] = - 900
Divide both sides so that you get "h" by itself:
h = -900 / [((1/tan(47)) - ((1/tan(35))]
h = same answer as using Law of Sines
The commitment of this man is absolutely amazing.
Thank you Professor Leonard, we really appreciate your efforts to make math easy.
I sure hope that you will eventually finish your differential equations course! Thousands of us out here can hardly wait!
the more we donate, the more effort he can dedicate to creating content
Professor, just wanted to say, you are the G.O.A.T.
Coming from India, economically disadvantaged, I can't begin to describe how helpful your videos have been to me and my friends. Thank so you very much for what you do, professor. Thank you so much. Forever grateful.
Thank you so much, as always. You are killing it on the videos recently! Literally, everything I am doing in class right now. Can't wait to see what other series you have planned.
Love you prof leonard
37:27 LMFAOOOOOOOO
😂😂😂😂😂😂😂😂
Lol I had no idea how to solve this years ago. Now everytime I see a volcano Im gonna try to figure out its height. Thank you, Professor, 💯
Professor Leonard ,thank you for another fantastic video/lecture on How to Use the Law of Sines in Trigonometry. The examples are helpful for a deep understanding of the Law of Sines. At the 55:12 minute interval and the final example, Professor Leonard, you use big C instead of small c. Please correct this error in the video. The Law of Sines can also be written as a divided by Sine(A) equal b divided by Sine(B) equal c divided by Sine(C).
How professor, are there no #30 & #31 for the trig series? I was going through the playlist and didn’t see them. Just wondering so I won’t be in the wrong order :)
These videos are great. Can you make some physics videos?
Is it entirely possible to use the law of sine and cosine for a right triangle? I just don't want to hassle with different methods.
At the event of AAA, how do you solve that? How do you solve x = x = x or even SSS?
💯
I just finished the last episode and now there is 32?
professor beckham
daddy 🥵
😅
Prof Leonard KILLING IT with the frequent video releases lately! Love it!! Keep up the great work, Professor!
1:16:21 Couldn't you just draw a line vertically down the middle of the triangle to make it 90? Two separate triangles, knowing that the angles of the triangles need to add to equal 180. Spiting side 5 into 1 and 4. Spiting angle 60 into 30
For the first triangle on the left, knowing 2 angles 60, 30 and 90 the angles of the first triangle is solved. Summing the angles equal 180.
Same goes for the second triangle as well, knowing 90 and 30 the 3rd angle can only be 60.
Side c for triangle 2 would be 32 as 4^2 + 4^2 => 16+16=32
Knowing that, for triangle 1 would be 32^2+1^2 => 64+1=65
So technically there is a solution. Right?
I was waiting for this topic. Thank you prof leonard
These vids are helping me a lot, keep up the good work professor!
Best of the best explanation of this important topic in Trigonometry. Thanks very much for this upload. Most helpful.
The best channel on UA-cam uploads again!
Very interesting! Thanks!
Thank you so much Professor Leonard for such quality videos ! You are a gem of a professor !
looking great!
sir!!! please make vids on curvature, evolutes/involutes, newtonian formula i am dying for your explanation
where do you teach ?
Thank you !
Sir.. Like always you killed it! Sir.. it's not necessary but would you please go back to your old hairstyle? this one is also amazing but the one you mostly keep looks like a kind of signature hairstyle.. it's not necessary but....
Stop analyzing his appearances. He’s here to teach us. How he looks or dresses is none of your concern.