Law of Sine Ambiguous Case

I introduce the Ambiguous Case for Law of Sine.
1 Triangle 2:12 and 23:00
0 Triangle 7:36
2 Triangles 11:25
Summary of Steps at 28:46
Law of Sine Introduction
Law of Cosine Introduction
Applications of Law of Sine and Law of Cosine

[lenena]

Thank you so much for these videos! With the quarantine making classes online, my trig prof basically stopped teaching and it's been really hard trying to learn these concepts by myself. Thank you for making them easy to follow and understand ^^

[everythingbuthair]

The story you told about your students when they don't understand the "calculator error" is the perfect embodiment of my frustration with math. I'm always taught just how to go through the motions and I've yet to even find a college professor that can really teach the idea. When I ask questions about the bigger picture or about proofs, etc, I'm more often met with statements such as "just trust me it works", "the formula is all you need to know", or "just do it this way" instead of any real passion about math theory. As a result I never know what's truly going on, I'm not connecting relationships of ideas to other math concepts, nor do I know how to think critically about the topic- so all the information gets dumped out the window at the end of every semester because I didn't really LEARN it. I'd do anything to think about math intuitively the way I can with chemistry. This is proving to be even more frustrating now that I'm in calculus because I don't see the errors I'm making, I typically have no idea how to start problems, and "designing" functions feel impossible at my level of understanding.

I know you're drowning right now with COVID, but if you are ever wondering what videos to make next, I would adore short or extra long form videos about any math (pre alg->differential eqs) theory. Around unit circle/euler's number it all starts connecting and feeling really tangible as a constant in the real world that can be used and I would love to hear you explain some of it. I'm sure even algebra is cool too and I just haven't been shown it yet! I know channels like 3blue1brown make videos along these lines, but if they pertain more to the sections of material I'm actually learning in school I feel they would help more in the long run to graduating in STEM. Would love your input on this!! THANK YOU for all that you do and keep up the amazing work!!!

[renewd]

That was a good and thorough presentation of a somewhat confusing topic. I did feel like the wrap-up at the end was difficult to follow, but I'm pretty sure I understood everything necessary to deal with these questions.

[chriswilliams]

For the second example is it a given that it is a right triangle? I did not see a 90-angle drawn, but I'm assuming the dimensions are the same as in example one.
A=22.62 degrees, a = 4 and c= 13
For example 2 would you be able to tell that the side opposite the given angle is less than the height if this was not a right triangle?

[shizzywizzy]

Looks like you're a Miata fan Mr.Rob! Luv your shirt with the NA, NB, NC, and ND!

[georgeseese]

Thanks for using geometry that shows the internal right triangle.
In the Cross Multiplication process, I see two right triangles I call RT1 (left side) and RT2 (right side).
You show how to get the opposite side of RT1 which is 'h' of the main triangle, to help determine solutions.
Consider the first example in the 2012 video, A47 a70 b62.
Cross Multiplication has 70sinB = 62sin47. Note that 62sin47 gives the opposite side of RT1 = 45.344 = 'h' of main triangle.
(Write that value down for solution analysis.)
That's the same opposite side of RT2.
So when I divide that opposite side (62sin47) by 70 (hypotenuse of RT2) I'm getting the Sine value of RT2 = .648.
Sin inverse .648 = 40.39 degrees, which is also the size of Angle B of the main triangle.
Please let me know if this is correct.

[ildaraliev]

Great job! Do you have creating video lectures about Discrete math in your plan?

[nathankassai]

Why does it look like you’re transcending in the thumbnail, lol. Great vid!

[bessermt]

I didn't know whiteboards came in black.