How to use SohCahToa continues, with a video on finding the length of a missing side in a right angle triangle.

Watch the video and try the quick test.

As before you can use SOHCAHTOA to calculate the length of a missing side, although, in this case, you’ll need to:

- know the length of one side
- know the size of one of the acute angles

A typical exam question would be along the lines of –

‘Calculate the length of the side marked ‘a.’ Give your answer to 3 significant figures’

With these type of questions itβs better to have a series of steps:

- label the side opposite to the angle
- label the hypotenuse (longest side)
- label the side adjacent
- decide which ratio from SohCahToa β in this question we are going to use Soh
- Once you’ve calculated –
**check it!**– side ‘a’ must be shorter than the hypotenuse. 6.43cm looks about right.

Many of the practical applications of this type of maths come from surveying – perhaps finding out the length or height of something when it’s very difficult to measure. Try this example; suppose we want to find out the height of a tower:

The surveyor can measure the angle, from 5m away, as 32 degrees. Therefore:

.. we can use trigonometry to find out the exact height – in this case the tan rule – Toa:

Using a calculator 5 x tan 32 = 3.124. So the height of the tower is 3.125 + the surveyors height of 1.72m:

Total height = 4.844m

**Total height = 4.8m (to 2 s.f.)**

Here’s some other posts that might be of interest:

How to use SohCahToa to find missing angles in a right angle triangle

How to work out the area of a triangle

Click here to try theΒ Quick Test SohCahToa

Heath Duivestein says

Thanks for a very informative and helpful video about trigonometry

definitely saved me from an upcoming test

christian butterworth says

Thank you again!!!!! Great help now pumped for the exam tomorrow

Salvador Velazquez says

thanks for the video

marshallpulham says

Sin being Opp Over Hyp wouldnt you divide the sin40 by the hypoteneuse not

times 10 man its been a while since ive done this

Pat Motley says

What do you do if the number you are dealing with is above the letter you

are finding on the equation? Is it multiply of divide?

pam2125 says

Lil different problem..If your treadmill is 6 ft long and is set at an 8%

grade. How high (in feet) is the front end of the treadmill?

Thanks

Treneice Walker says

What do you do when its cos instead of sin beacuse my promblems is asking

me to find the missing angle by using cos π

Lizzy X says

Thank you so much, I get it now!:)

Feras Sabri says

if I have 2 angles on a triangle and they asked me to find length what to

do >>??

Gabriella Gomez says

thank you so much this was extremely helpful

jacob lowe says

Thank you

Mikey says

You seem like a very nice man ! Also great video mate. Come on you irons?

Srinivasa Yasa says

this helped a lot thank you

ajoksable says

i dnt really understand this sir thanks

KatelynNicole226 says

Thank you SO much I missed a day of class and I used this video to catch my

self back up!

John McGuire says

Very helpful, thank you. Now I’m just looking for when you use Cos or Tan

to find either the hypotenuse or adjacent. Also solving for when one side

is labeled “X” or “X+2”. Knowing the difference between adj and Opp and

knowing when or how to use it.

Glerize Anne Mallanao says

thank i can past my test

Eden Harbour says

This was so helpful! Thank you so much!

Lawrence Ah-Weng says

I used this to try and find the hyp in a gcse calculator paper but I got

12.85575219 which wasn’t bigger than the opp so is it wrong?!

Chima Amobi says

epic stuff you have helped me out alot ;-), but when i checked my

calculator i got 0.64 is that correct?

Epicnerd73 says

I liked your construction example, it helps people appreciate that this

stuff is actually useful in real life as a lot of people in my classes

don’t appreciate maths and think it’s a waste of time π

Alan Sumpton says

Really helpful, thanks a lot π

Sydney T says

i got 7.45

dashaneil henry says

A man walks x km, due north, from point G to point H to point F. The

distance along a straight line from G to F is 13 km. (a) from the

information, write a equation in x which satisfies Pythagoras Theorem. Show

that the equation can be simplified to give X2 +7x -60=0 >>>could yoe solve

this please

Daniel Harris says

Thank you so much you have just clarified the part i was stuck on.

hadi farrukh says

fanatastic explanation. you are an immpecable tutor to say the least.

Z3NTR0 says

what if i get a question where it doesn’t state any angles but tells me for

example, the hypotenuse and the adjacent. because these sorts of questions

are going to be on my exam

Starpilot149 says

This really helps man, thanks.

aaron ho says

very helpful

Ashton De Jong says

Thank you so much! I was so confused before.

stephen barker says

whats the best way get a* or a in gcse maths

stephen barker says

how do you know if you have to divide or multiply

Ryan Callahan says

Great video, very helpful!

stephen barker says

when you work it out is it always 10 x sin 40 or can you do it the other

way round

JΓ₯sΓΈn Γ says

I posted a question on one of your other videos. Building things, I usually

know two desired angles and either O or A. Hardly ever (if ever) known the

Hypotenuse as it’s normally the value I’m trying to find. Usually know

angle a, b, and length O or A. Can you tell me what I need to remember for

this? ie. I have a support that connects at 1800mm high, set out at an

angle of 15ΒΊ from vertical. So how far out will it be when it reaches the

floor? a=15 b=90 c=75 O=1800 A=? H=?

JΓ₯sΓΈn Γ says

I’m trying to find H and A. O=1800mm The building roof example is good –

but when building most things, you’re less likely to know the H and more

likely to know the O value (in height) or the A. So using the H as a known

length seems unlikely because it’s usually the one you can’t reach. Can you

show this again with the A or O value known?

Naif Sayyaf says

Thank you for this. <3

David Johnson says

sir is it possible that only the opposite side is given with an angle of 90

deg.?

Thomas Russell says

Actually helped me a lot with GCSE mock exam … Thanks! π

drumman Murchie says

getting stoned on maths wrap

Lori Zaitz says

(I’m using my moms youtube right now) omg thank youuuuu! your video saved

my math final grade! and just to let you know, there is an extremely high

pitched feedback your mike gets when you talk, I just thought you should

know. Thank youuuuu!!

Thomas Butt says

Thankyou so much π

second gom says

nice beginning

π

Storm Low says

Great video!

70carlton says

Thank you so much Simon very helpful.

Diztriction Tableflippa says

Thank you, helped me!

John Hereford says

*students

John Hereford says

do you want a job?

– De La Salle High School

arjun Sidhu says

thanks for the help but another question i am confused with. it is that i

have 2 lengths of 14 cm and 5cm and i have to find the length of the other

side of the right triangle

GeorgePosts says

Thanks Simon

Melissa Saintlot says

its hypotenuse

cheryl robley says

excellent tutorial, thank you I seem to have cracked sin.. however when I

need the adjacent and have an opp of 3.1cm and an angle of 25.6 degree and

use TAN I keep getting 1.485 which doesn’t seem a reasonable length, id

have guessed more like 6cm?? any ideas where Im going wrong?! could it be

because adj is the denominator not the numerator like when you do sin?

thank you very much hope my question makes sense!

Big Papi says

thank you so much!

jmitsch44827 says

Good explanation, bad audio. Please fix.

dayal manger says

thanks really helped alot

Sharyaar Bhatti says

thank you soo much

LazymonkeyIndustries says

Thank you very much for this tutorial sir . It’s very helpful especially

for my upcoming finals π

Steve Ballmer says

Great video man π

keep it up!

AM moses says

Thank u so much!!! U saved me!!!!!

Andy Nguyen says

Thank you for your great explanation. This really helped me out a lot!

Simon Deacon says

Please like and leave a comment!

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

zv3000 says

Hi got a question probably a bit impossible to work out but what if the

information you have is just the adj and opp besides obviously the 90* ?

imagine the adj is 53.34 cm and the opp is 10.16 ?

Charlie Parker says

what formula should I do if its given me the angle and the opposite instead

off the hypotenuse ??

Osvaldo D says

Thanks, wouldn’t have done my math project without you :-).

john hanley says

thanks again

JamesTheBaker says

Thank you so much, this was the only area of trig that I wasn’t too sure

about, even though I did know how to do non-right angled trig

Simon Deacon says

That’s great – thanks for letting me know π

Dana Perry says

I struggled so much with this but you helped me so thank you π

Simon Deacon says

Glad to help π

Simon Deacon says

Keep working through questions and you’ll be fine. All best S

Nezerrath .Gaming says

oh my god the complication but i’m gonna try my best. thank you π

dracoclash says

(T-T) thank you so much!

Simon Deacon says

Hi – I think that your calculator is set to degrees rather than radians. (Radians are a different way of measuring an angle and some calculators will allow you to work with either). All best S

Simon Deacon says

Please post, pin, tweet, like or subscribe!

Simon Deacon says

Please post, pin, tweet, like or subscribe!

buehlerbri says

I did 10 times sin(40) and I got 7.45 what am I doing wrong

Josie Prada says

such great help ! π

Simon Deacon says

Hi yes Cah would work fine if you had the hypotenuse and the angle …make sure it’s the one adjacent to the adjacent side you are working out. (Hope that makes sense :-).

All best

S

23FlukeShot says

if im given a right angle triangle which asks me to find the missing side in my question the hypotenuse do i use the same method that you did except with cosine in this case?

Ian Long says

love your tutorials, would be really good if you could write a bit bigger for the eejits like me that can’t see that well though. Ta.

Simon Deacon says

Hi – thanks for the question.

The way SohCahToa works is with the relationship between the angle and the sides. The problem is the opposite and adjacent will change depending upon which angle you’re using. With these sorts of problems it’s probably better to label what you know, then work out if they are opp, adj or hyp, and then go from there.

I hope this helps.

All best

S

billybobdog5 says

why did you use sin 40? why not sin 50? that’s the only thing confusing me

John Rivoski says

Thk You SimonDeacon

John Rivoski says

th

Simon Deacon says

Hi Zain – you’ll need to know either the length of an adjacent side or the angle to use SohCahToa. If you send me the question (through MathsWrap if easier) I’ll will be happy to help π All best S

zain ali says

what if the hyp is 100 ??

Simon Deacon says

Hi – sounds like you might need to use Area = 1/2abSinC. Use this to find the length of b although you’ll need to change the equation around a little bit.

I haven’t got a video for this but there’s quite a few on YouTube.

I hope this helps.

Best

S

Alfred Chan says

If im given one angle, one side and the area, how to do i find the rest? (its a scalene triangle)

Katrina Brown says

Thanks you helped a lot:)

Simon Deacon says

Hi – yes, you need to use the inverse on a calculator to find angles.

marco s says

do you only inversese sin cos or tan when your finding the angle inside?

Libaan Ahmed says

Thanks so much.

Simon Deacon says

Hi Russell – yes, the concept is still the same. You need to know one angle and one side to find another length … sometimes there’s a bit of calculation first to get all the info you need.

Russell Siete says

Denominator / Numerator Sorry flip in words lol.

Russell Siete says

You only multiply the Numerator. But say if I don’t have my Hypo, but rather the Adjacent? Is the the concept still the same? Probably, but what do I do if I have Denominator? Dividing is probably my choice…which I have a difficulty on how to do that. lol

john zitro says

this one i get the formula and the calculation..

Simon Deacon says

Great – thanks for letting me know π

Jamie Morgan says

Cheers mate really helped π

Ismael Djibrilla says

thank you so much π

Ismael Djibrilla says

thank you so much π

Bridget Canavan says

Thanks this is a really helpful video!!! I get it now!

π

Simon Deacon says

That’s great – glad it helped and thanks for letting me know π

Marco Deleon says

Really helpful video!!!!!

XDinaChowX says

OMG this was soooooooooooooo helpful! I’m found GCSE maths and I had no idea how to do this trigonometry SOHCAHTOA thing! This video really really really helped! Thanks so much!! :

Simon Deacon says

Hi – latest video – please let me know what you think.. Thanks!