## ‘How to use sin, cos and tan to find the size of an angle in right angle triangles’

.. can seem a little daunting.. but they are used extensively in maths and have some real, practical applications.

Watch the video and try the quick test.

##### Click here to try the Quick Test SohCahToa

You can use sin, cos and tan – some of the “trigonometric functions”

- to find the size of an angle in a right angle triangle or
- to find the length of a side in a right angle triangle (more about this in the next post)

To find the size of an angle you need to know the lengths of two of the sides.

For a right angle triangle the sides are labelled relative to the angle you need to find – in other words, ‘opposite’ is opposite. So:

### A typical exam question would be something like:

“Calculate the size of angle x in this right angle triangle. Give your answer correct to 3 significant figures’

With these type of questions it’s better to have a series of steps:

- label the hypotenuse first (longest side)
- label the side adjacent to the angle you want to work out
- label the side opposite to the angle
- use SohCahToa – in this question we are going to use Toa

**inverse trigonometric**functions.

- make sure the calculator is in degree mode (look for D symbol on your display)
- Use the inverse trigonometric function and brackets for the ratio

**To 3 significant figures: 39.8 degrees**

Trigonometry is an really useful part of maths and is used in architecture, building and all sorts of construction. From finding the heights of trees, towers or ocean tides to navigation, physics and astronomy – you’ll find some trigonometry.

Did you know that the ‘trig’ bit means ‘triangle’ and the ‘metry’ bit means ‘measure?!’

Watch the videos on YouTube:

How to find the missing angle in a right angle triangle

Ali says

There is a typo on your page under Trigonometric Ratios above; Tan = TOA not TOH,

Thanks for your excellent lessons, really appreciate them

Simon says

Ah. OK – will change.

siosifa vaitohi says

Hypotenuse

Yaqub HDGamer says

do you need the minus one for cosine and sine?

Bonheur Ntwari says

when he teaches better than your school teacher

razoractive02 says

ok you did not explain why you had to use the inverse… this will confuse

a lot of people

kuda deka says

thanks it helped me so much

NHD14 says

THANK YOU!!!!!!!

Naazim Jehangir says

Thanks For Helping me understand trigonometry! no teacher is better than

you

your students are lucky +Simon Deacon

Subscribed Aswell

christian butterworth says

Thank you so much for the help and am sure I will be using these videos

again for a-level

Victoria Davies says

Thank you, this helped so much

Versace Cakes says

bruh I need this for my final tmw

Big M says

Thanks this helped a lot

Austin Maupin says

Question… This bothers me that I don’t quite understand it but, Why is it

that when I type Cos-1(3.9/4.7) it comes up with 0.592069997?

Zinedine Zidane says

thank you so much

Daniel Preston says

Thank you:)

GoProXadventures says

In America, the spelling is “hypotenuse” but I don’t know what it is in

England 🙂

MrSmithWashington says

Thanks this will help me with some last minute homework.

Christopher U Ren says

Hi there how come when I type in sin-1(3/2) it comes up with maths error?

Chris Ott says

thanks for actually teaching me, my teacher sucks

Ethan James says

thanks, great, u helped me so much with my maths notes

TheOneandOnly , says

Thank you, You are very helpful!

AliceIn APalace says

thank you this helped me so much 🙂

yoali ramos says

How is it that you know what’s the opposite located?

Valor Gaenz says

This video was so helpful! I’m definitely subscribing and will surely be

back for more!

Ben Lowther says

Very clear! Helped my revision massively, thanks! 🙂

Mohamed Yousif says

Have a Math Test tomorrow and was feeling confused about the topic. You

helped clarify things!! Quick question, am i supposed to put (-1) after

which ever one i use for example Sin(-1)?

Sir StubbedToe says

Thank you, this was a nice refresher to help me with my homework. I really

appreciate what teachers like you do when you make these videos, they are

extremely nice when others like myself may need some help or a reminder on

how to do something on short notice. Thanks to you we have a teacher in our

pocket now!

Joe Howarth says

Brilliant nice one

karl bermillo says

Thanks! This was really helpful. I have my final exam tomorrow. Subscribed

^_^

Ruth Ayodele says

Thanks your teaching helps alot

Shania Pindoriya says

Thanks for your help. When do you use the inverse trigonometry? E.g. tan-1

or for sin or cos? Thanks again

ETrademarkk says

Thanks, helped refresh my memory for my ACT practice! 😀

LRichmonde Bupper says

thx this will really help me tomorrow for my maths test 🙂

Rachel Jackson says

This was a really helpful video thank you! I’ve been sent through

accelerated Math/Calculus since I was about 7 and we’ve only realized now

that I missed out the entirety of SOHCAHTOA…. and I’m in my last year of

school 🙂 So thanks for the help

matt arthur says

Thankyou!!!!!!! I went from zero knowledge to full on I know what I’m

doing! Thankyou very much!!!

Dexterihty says

thank’s for this video it really helped a lot with me missing class

Aboubacar Kone says

I know how to do trigonometry now +Simon Deacon

Stuart Campbell says

Subscribed:) watching your videos are really helping me with my maths gcse.

Thanks!!

John Willard says

Thank You!!!

oisin mcmanus says

Thanks! Great Help

Ben Horvick says

This helped me cram right before my ACT test. Thanks!

Jairaj Surnam says

I don’t get it

Grace Luce says

Thank you so much! I had missed a whole week of my geometry classes and now

it all makes so much more sense!

Dylan Wyatt says

Thanks skrub lord

ajoksable says

lovely sir but i dnt really understand this sohcah, pls wht can i do thanks

Raheem Ssejjuko says

hi , I done exactly what u said and ended up with a different answer which

was 37.69234667 – 37.7 +Simon Deacon

Avraham Saltoun says

very good

danish pace says

At first I didn’t understand it but after 30 minutes i realised just how

simple it is!

ThatNerdGirl says

Thanks I needed to learn this for my placement test

daniel cummings says

DemandingWaffle | Fifa 15 Content & Gaming Tutorials! says

hi im having a problem when i type in cos(3.9/4/7) on my calculator it

comes up as .99? why?

Ben Target says

can you use any of the three different things the same way?… the SOH,

CAH, TOA so for instance if i only had the opposite length and the

hypotenuse length would i use “SOH” in the same way as “CAH” (Using the sin

and sin-1 button on my calculator..)

Vanessa Lennard says

I’m a bit confused how to know when to use to the power of -1 or not for

sin, cos and tan. Do you something basic to explain it?

Thanks

Ballistic Bricks says

Thanks I forgot to put it to power of -1

kwesi martin says

Thanks bro, you have been really helpful. Like your teaching strategy!!!

Reda Elazouar says

Amazing help. Thank you so much.

CJBgb13 says

Thankyou, I was really worried about my exams but you have cleared this up

for me

Caderious Davis says

Thanks so much. This was so helpful to me. The way my teacher showed me was

a little more complicated. This hit it right out the park.

Lynx HD says

Thankyou best this was explained very well much better than my math teacher

did I thought I was going to fail my test. Thankyou!

Louie Wright-Grant says

Thank you. Really clear and helpful

Jonathan Balderas says

You are a saviour

MegaProdigy21 says

Thanks so much because I was stuck on my geometry!

Apiraamy Murugathas says

You’re seriously so helpful. Thank you so much! Ive also subscribed to you!

😀

jamie stewart says

Simon deacon is god

aaron ho says

really helpful thks

JESUSISGREATEST says

Are you a math teacher?

superkhayvii says

hello. i have a question..

A 10-pound object is suspended by a string from an overhead support. A

horizontal force of 5.8 pounds is applied on the object. The measure of the

angle which the string makes with the horizontal is??

a. 30 degree

b. 45 degree

c. 60 degree

d. 90 degree

the answer is 30 degree..

but I don’t know the solution. help? 🙂

thanks in advance!

superkhayvii says

hello. i have a question..

A 10-pound object is suspended by a string from an overhead support. A

horizontal force of 5.8 pounds is applied on the object. The measure of the

angle which the string makes with the horizontal is??

a. 30 degree

b. 45 degree

c. 60 degree

d. 90 degree

the answer is 30 degree..

but I don’t know the solution. help? 🙂

thanks in advance!

Googly787 says

thanks!

Hitesh Bhardwaj says

Did you make your website ???? If yes could you possibly upload some C# or

C++ or game maker scripting if possible

Thanks

Mohammed Al-Bashiri says

Thank you

Daniela Rodas says

Hi Simon,

Thank you for this video but when I typed in cos-1(3.9/4.7) I ended up

with .592069997… What did I do wrong?

Usman Khalid says

thanks bro this really helped

Eleanor Lane says

A brilliant refresher for me thanks!

Preston Ellis says

can you be my teacher 😀

Janett Omeally says

Thank you sir, this was helpful

Paaryn Vadgama says

Is it just me or are videos online a trillion times better than teachers?

Thanks Simon!!!

Naif Sayyaf says

Excuse me Simon, why do i get Syntax Error? Is there any other way to solve

that?

Ciaran Lewis says

Thanks Simon for another great video. Would I still get the same answer if

I accidentally left out the brackets that you did in 7:01?

stephen barker says

have i got this right if the angle is attached to the hypotenuse and

adjacent its cos if attached to the opposite and hypotenuse its sin and

opposite and adjacent its tan

stephen barker says

i remember it by the side the angle is attached to is the 1 you use

Jack Footy says

Thank you so much ! By the way, you always use the -1 to calculate angles ?

Thanks again ! Finals tomorrow so this will help.

Michael Morales says

does SOHCAHTOA only apply to right triangles?

Wind Ofstorms says

Thank you this helped a lot.

NeU guir says

Thanks for the help! Very easy to understand now, thanks.

Jonty Wispinski says

Nice and

quite helpful thnx xD

stephen barker says

im trying learn trig in 3d

Cody Ivy says

My calculator sucks balls

Sam Dore says

Thanking you for my top marks in my Math exam!!

stephen barker says

i dont understand where the minus 1 comes from

stephen barker says

what if your only given the value of 1 side

stephen barker says

i remember it as cos angle is attached to adjacent and hypotenuse sin is

hypotenuse attached to opposite and tan adjacent attached to opposite

Dharmendra Patel says

even though your videos help me a lot there is one concept of math science

called pre-calculas sorry if i spelled it wrong, but you should think about

making a video on that thanks anyway! 🙂

Matt Foss says

Thanks so much for this video! It helped me out a lot!

70carlton says

hypotenuse doesn’t matter we’re in a math class not a grammar 🙂 very

helpful thank you

70carlton says

very helpul video

70carlton says

hypotenuse

Grace Ramirez says

Hey , so its tan1 divided by 5/6 then thats how you get your answer?

langgapu says

i dont know y its so different into my computations? instead of 39.805

should the right answer the answer on my calcu is 1.100 please help me..

Taia Hopkins says

Why did you use the (tan -1) instead of the regular tan?

Brandon Munemo says

Thank you so much got an exam tommorow and i think this is very useful

Choco Trevor says

Thanks Simon really helped

Jessica Laurens says

OMG thanks soooooo much I have a huge exam and this is a small part in it

but was also the part I have no clue about! Thanks so much, you make so

much more sense than my teacher 😀

VolkswagenDude181 says

Great video! It helped me immensely! thank you so much

SpartanIV says

Really helpful video! Thank you very much!

drTHEAWESOME says

Simon I don’t know if you will ever respond to this comment ever even look

at it but I won’t you to know that you may have double handily saved my

mark on the test and i wan’t to make love to you!

Rosie Smith says

Thankyou! Really helped xx

Jangwoo Lee says

The spelling is hypotenuse, not hypoteneuse.

medicinegone says

Hypotenuse, just like it sounds.

Emily Janes says

Thank you! GCSE maths revision is hard but your videos make it really

simple!

technoman232 says

my only question here is that I though that when you are trying to find the

ANGLE in the Triangle why did you not do SHIFT 4.9 Divided by 4.7?? thats

at least how i Learned to find the Angle, cus I thought that if you dont do

the SHIFT on the calculator first then it wont give you the complete answer

to the Angle.. lol, I live abroad and Im in 11th Grade, I learnt this at

the beginning of my school year and now im just Reviewing it over and over,

and i wanted to check online if other people Calculate this like me..

chito pusak says

You’re good but the video cam is somehow blur…I can’t see the exact words

or numbers…but thanks you’re great!!!

Simon Deacon says

Please like and leave a comment!

Visit https://www.3minutemaths.co.uk for real maths, tips and techniques.

Rhys Samuel says

Thanks man great help

Melvin Bowen says

There has to be some way you could possibly find this info without a

calculator.

Joe says

thanks a lot!

Bubblee Frog says

Thanks for your help!

john hanley says

but good video mate thanks for helping with me homework

john hanley says

You spelt it wrong its Hypotenuse not Hypoteneuse lol

Michael Nguyen says

I got .694738 what did I do wrong?

Lawrence Alvarado says

Thank you so much, this video helped a LOT! 🙂

Manshah S.Dawood says

how did you calculate 10 times sin 40 degrees using the scientific cal.

which button to use. Thanks

Boby Gandhi says

which calculator do you have? on most you can use shift then cosine button for cos-1 if thats what your looking for…but google is your friend for how to use a calculator

Boby Gandhi says

one angle is right so it is 90 degrees. so if you can find one of the other two using trig then the last angle is simply found by adding up the sum of the two angles(90+ x ) and then subtracting by 180.

Simon Deacon says

Please post, pin, tweet, like or subscribe!

Simon Deacon says

Please post, pin, tweet, like or subscribe!

Simon Deacon says

That’s great and glad to help 🙂

Erika Andrea says

Awesome video! Very helpful. Thank you 🙂

Sunday Jammers says

What if the you need to find two angles?

Marek Wegrzyn says

nice u just explained how to use calculator impressive

cuteandsporty says

Thank you! Very helpful 🙂

TheStatueOfLibertyy says

YOU ARE SUCH A NICE MAN! HAVE A NICE DAY 😀

Simon Deacon says

Hi – the symbol you’re looking for is cos-1. My calculator shows it in orange print and I need to press shift first. Hope this helps and thanks for the comment. Rgds S

PRINCE LEGIT says

How do you cosine to the power of negative 1 on a calculator ?

Matteo Bro says

If anyone’s tripping up with the wrong degree thing, check your calculator’s settings. It might be on “radian” instead of “degree.” That’s why mine messed up on this also.

Simon Deacon says

Hi – some calculators use different notation but you’re looking for Tan-1. This is the inverse of Tan and, on my calculator it’s printed in yellow. My buttons are Shift Tan – this gives me Tan-1 (

I then type 5 / 6 and close the bracket.

My display reads Tan-1(5/6). When I press the = I get 39.805…

I hope this helps and all best with the ACT!

Rgds S

Kevin nguyen says

I’m pushing buttons 2nd, TAN, (5/6) but it equals .6947382762. Please help!! I have the ACT tomorrow!!!

Cheyenne Simpson says

Great video! You really helped me! thanks 😀

ForeverInLoveXOXOXO says

Thank you. Very helpful 🙂

SamOwenNewton says

You explained this better than my teacher, thank you!

Adriatix Prowsman says

thank you so much man saved my life once again

Simon Deacon says

That’s great – thanks for letting me know 🙂

Sam Casey says

Thank you that helped a lot

NadineJonas101 says

So helpful for my exam! Thanks so much

Simon Deacon says

That’s great – thanks for the comment 🙂

dadiddumsfish1 says

this really helped to get sohcahtoa clear in my head:))) thankyou!

Simon Deacon says

Sorry.. no.. we’re doing a lot of GCSE (same as Regents?) revision so lack of time. Good luck with your finals!

Antoinette Marie says

Did you make the video yet? I have finals tomorrow. Integrated algebra. :$

Antoinette Marie says

I subscribed

Simon Deacon says

Will do – I’ll let you know when done. All best with your studies. S

Antoinette Marie says

Oh and can you do a video on how to simplify radical expression and adding radicals

Antoinette Marie says

Ohhhh thanks! I have regents coming up next week. Do you know any topics that always reappear on the regents?

Simon Deacon says

Hi – hypotenuse is always the long side. The adjacent is next to the angle you are working on. Its always good to re label the diagram each time, so hopefully not too confusing 🙂

Antoinette Marie says

So how do we know whats the hypostnuse and whats the adjacent angle?

Libaan Ahmed says

Thanks so much.

Tobias Fitzsimmons says

Thanks, the video was very helpful and made trigonometry incredibly easy to understand.

jontealex13 says

can you make a video showing how to use the calculator when you are doing this because i cant get out the answer

Simon Deacon says

Thanks Sammie – I’ll try to remember 🙂

Sammie Louis says

hypotenuse

Simon Deacon says

Hi John –

The number you’ve got is the tan value.

Calculators keys can be a little different, but try this: Shift, Tan, (5/6). Sometimes the command to get tan to the power of minus one is printed on the key in orange.

Hope this helps and let me know how you get on.

All best

S

john zitro says

why it is always wrong answer when i press tan-1(5/6)? the answer is always 0.014545436094.. i didnt know what value i type..

john zitro says

why it is always wrong answer show in my calculator? it show the answer 0.014545436094 if u press tan-1 (5/6)?

Simon Deacon says

Hi – no prob and good luck with the exams

mrdeadduck456 says

thanks man this is just what i need to help me understand trigonometry for my summer exams. ur a life saver man thanks 😉

Simon Deacon says

That’s great and thanks for your comment. Good luck with the job! 🙂

slowrides78 says

Just wanted to thank you for posting your very informative videos . I needed to relearn a lot of basic math for a job placement test and thanks to your lessons I passed with no troubles .