Trigonometry word problems (part 1)

[xMrsFamous]

Are you Asian?

[xMrsFamous]

way too complex when u could just use the cosine rule...

[DarklightALBANIA]

Thanks a lot Khan trigonometry used to be a weak point for me since I met you

[thefurquan101]

Not getting this :(I get confused when you organise the equation 5sin 43 or sin 43 i don't know please help

[9jar9]

official 4 yeas since you made this video yay!!!!!!!!!

[anitha6560]

verrrrry easyy way 2 learn!!!!!!!!!

[WishFredWasDead]

Pythagorean theorem...???

[MrMGD92]

@WishFredWasDead it means A squared + B squared = the square root of c.so on a question if you figure out A measures 5 and B measures 6,to get C you square 5(so you do 5x5 = 25)and B squared (6x6 = 36)add them together to get 61,then you find the square root of 61 to give you what the C angle is.Khan talks about this on a video.(I think it`s called introduction to algibra)I think I give it to you right but it`s worth checking out just to be sure :)

[MegaBEANER1000]

couldnt u just use the Pythagorean theorem

[xMrsFamous]

@MegaBEANER1000 You can only use the pythagorean theorem when you have a Right Triangle

[darknightprince18]

do i have to use the Pythagorean theorem? i guess i have to use square roots like this Csquared = square root of Asquared + Bsquared....is square root is not applicable to that?..or does pythagorean theorem is not needed to that.? reply plss

[darknightprince18]

@darknightprince18 ooops, sorry about that haha,,,i didnt finish watching this so i thought you dont use square root haha

[4321ba3g]

4:12 is in it ment to be sin cuz its sin= oppsite over hyptonuse ?

[triciatriciahaha]

"let me pick a nice color" yes lets pimp this triangle

[ferdawz1]

i m also khan!!!



[kungfufreak360]

@ferdawz1 khan is a very popular name

[HappyMilichi]

Oh my gosh, thank youuu!!! This makes so much more sense now!!!

[basit311]

please write like a human

[junior1984able]

u got to write yr wors better .

[rachevirata]

my head ache a lot... hahahaha

[rickybears]

Funny how he changes his voice, when he is teaching and when he is making comments . XD lol. ISN'T EASIER TO USE MATH 0 ? ON A SCIENTIFIC CALCULATOR ?

[spazolio]

What I found to be very strange, is that I also chose the remaining side to be M, before I heard you say it. After the tingly feeling went away, I decided to figure out why we both chose M! Obviously I can only speculate, ButI think it was because we had point A and point B already plotted, and also X, Y, and Z., I think we decided to chose a letter that was completely different from A,B,X,Y,Z, and therefore our Brains opened the filing cabnet, and chose M from the exact middle of the alphabet

[spazolio]

What I found to be very strange, is that I also chose the remaining side to be M, before I heard you say it. After the tingly feeling went away, I decided to figure out why we both chose M! Obviously I can only speculate, ButI think it was because we had point A and point B already plotted, and also X, Y, and Z., I think we decided to chose a letter that was completely different from A,B,X,Y,Z, and therefore our Brains opened the filing cabnet, and chose M from the exact middle of the alphabet

[May199305]

thanks alot for all the video, it has helped me alot!

[brianaanicolee]

i love hearing this!!! you make math way more fun than it is :)))

and wanting to be a math teacher you have helped me allot

learning new ways to communicate with the kids

[smithyboy81]

I love this guy!!!!! Khanacademy if you are reading, I would love you to know that you helped me a lot. I am a what you would call a mature learner, and what you have shown me has got me ready for going back to university.

[flyingbeagles]

This is the most charitable thing to do, I think its more empowering than than money

[severelyaddictedgal]

You're sense of humor lightens up the math problem.

[michaelchukwu22]

cosine rule would have been better and faster

[19t]

u are the best !!!!

[angieblack951]

I LOVE YOU!!!! Thank you soo much! your work is amazing i really appreciate this. Thank You

[linhlinhpham]

couldn't you have use the law of cosines on the first problem?

lets call the ship point c

(CB)^2 = 5^2 + 10^2 - 2(5)(10)cos15degree

[agravainesunicorn]

thank you SO much for this. saved my butt.

[doritoesPLAY]

I dont understand what he does from 8:05 to 9:45 ... he squares the yellow writing i get that but what did he do with the red?

[flyingbeagles]

@doritoesPLAY I think he took the step to show the result of expanding the red part (which he didnt for yellow because that was more simple I guess) you can see how he got that when you expand it

(10-5cos15)(10-5cos15)

[rogerwaitout]

I would hate to sit in a classroom with this person for more than 30 minutes

[Catkill666]

Couldnt you just use the cosine rule?

[PullyElbow27]

@Catkill666 Technically yes, he could have, but I don't think he taught the Law of Cosines yet when he made the video.

[Catkill666]

Ahh i see, Im quite happpy i noticed that though

[FireBenderKwyna]

You are my hero.

[2SHEA]

any videos of a right-angled triangle being cut into half(but not seperated): having only values for only 1 of 2

seperated triangles.

e.g:

tri ABD, where ABD = 90degrees

A produces a line where it meets at BD, calling it C.

The line AC, hence, made 2 triangles in 1.

Having AB=12, BC=5, AC=13, find cosACD.

hope that explains the question, any help? i'm stuck.

[Nickshark1982]

Got lost on that one! Will watch again and again and again

[ViolentSkar]

Thank you so much, this video was really helpful, you explained it alot more simplier than my math teacher -_-

[Blueknightex]

Lolz I almost got lost on the y-part cuz I thought that the equal(=) sign looked like a minus(-) @_@

By the way Khan how come you like skipping steps and just subbing it in the end? :(

[MyOverflow]

A new side of a triangle: The Oppotenuse!

Thank you, Sal. :)

[boym0n2]

theres an h in hypotenuse

[FalllikeDisco]

if you don't mind me saying something...

it would be less confusing for people watching this if you finished the equation of x and y and z first before you continue. So people could get a better understanding of how your completing these equations.

[actionjessie]

I got confused at the part where you said "if that confuses you" how do you get 100 - 100 cos I understand 5 sin 15 squared is = 25 sin 15 them + (10 squared) 100 then confused at - 100 cos 15?

[TonyIommi07]

Think of it like this. What is (x+5)^2? Because (x+5)^2 is the same thing as: (x+5) * (x+5) Therefore expanding it gives you: x^2+10x+25 An easy trick is to square the first term, then multiply the terms and double it, then square the last term. So (10-5cos15) Expanded= 100-100cos15-25cos(15)^2 If it's still tough, let (cos15) = x and do it like so: (10-5x)^2 =100-100x-25x^2 =100-100(cos15)-25(cos15)^2

[thelegendofwiked]

without knowin this is a trig course though how would you think of usin trig

[InfinitelyManic]

This problem should be easy to solve using Law of Cosines because you are given the answer to one angle and two legs; therefore, you can use a^2 = b^2+c^2-2bc*CosA. If A =15, b=5km and c=10km then take the square root of 5^2+10^2-2(5)(10)*Cos(15) to get about 5.3 km.

Thus the boat needs to travel about 5.3 km after changing heading by about 14 degrees to get back on course. The 14 degrees may be found using Law of Sines; a/SinA=b/SinB=c/SinC.

[SkullX01]

u said A=15, b=5km and c=10km this is does not make sense.

instead say angle A = 15 deg, AC = 5 km, and AB = 10km

[InfinitelyManic]

I think it is does make sense and it is certainly acceptable given the context; namely, the Law of Cosines and Law of Sines. 

Is it more correct to say "you" than "u"? Both are correct as long as your communication is understood by its receiver.

Otherwise, I am missing the reason why it is does not make sense.

[pantboy100]

you lost me at the drawing the line down the middle of triangle part

[miterbinsderty]

Cos he traveled 5km/ 10km its an iscoceles triangle so cant u just do

180- 2 times 15 = 170 divided by two = 85?

[OOBKO]

Can't u just do the cosine? a^2=b^2+c^2-2abcosA

[TmSensis]

That would mean:

x^2 = 5^2 + 10^2 - 2*5*10*cos15°

which would give x~5.329

[TmSensis]

but you could use the cosine rule

c^2 = a^2 + b^2 - 2ab * cos(gamma)

[bradkey98765]

why not use the sine rule? ... .

[TmSensis]

because you need two angles for the sine rule!

[818coolkid]

sin rule (the law of sin) is sinA/a= sinB/b= sinC/c right? maybe he is not there yet. but he could also use sine instead. which after 5 minutes of looking for law of sin, found out you probebly ment that.

there is also a third way which is the law of cosine. which is much easier. MEN I LOVE TRIG!!!

[bradkey98765]

How is the cosine rule easier?

[818coolkid]

because, law of cosine is different than what this guy is talking about now.

it's about if you have two sides and one angle, you can easily solve for the other unknows side.

[danielhan2007]

that is where the cosine rule came from.........ㅡㅡ;;

[jaysin1947]

suck...i can solve this prob in jus 1 min...or better a few seconds..see the international level probs ..they rock!

[kyu012]

lol @ "that's a nice ship." give yourself a nice pat on the back, sir.

[lilwhiteplum]

good vid! Thank you for helping kids like me XD

[wumby]

Looks pretty good! Good example, it helped show some application to this math.

Wouldn't just using the law of sines be faster and less complicated?

[desoan]

... you cant?