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 it’s 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 – 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 the Quick Test SohCahToa
Thanks for a very informative and helpful video about trigonometry
definitely saved me from an upcoming test
Thank you again!!!!! Great help now pumped for the exam tomorrow
thanks for the video
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
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?
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
What do you do when its cos instead of sin beacuse my promblems is asking
me to find the missing angle by using cos 🙁
Thank you so much, I get it now!:)
if I have 2 angles on a triangle and they asked me to find length what to
do >>??
thank you so much this was extremely helpful
Thank you
You seem like a very nice man ! Also great video mate. Come on you irons?
this helped a lot thank you
i dnt really understand this sir thanks
Thank you SO much I missed a day of class and I used this video to catch my
self back up!
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.
thank i can past my test
This was so helpful! Thank you so much!
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?!
epic stuff you have helped me out alot ;-), but when i checked my
calculator i got 0.64 is that correct?
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 🙁
Really helpful, thanks a lot 🙂
i got 7.45
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
Thank you so much you have just clarified the part i was stuck on.
fanatastic explanation. you are an immpecable tutor to say the least.
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
This really helps man, thanks.
very helpful
Thank you so much! I was so confused before.
whats the best way get a* or a in gcse maths
how do you know if you have to divide or multiply
Great video, very helpful!
when you work it out is it always 10 x sin 40 or can you do it the other
way round
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 15º from vertical. So how far out will it be when it reaches the
floor? a=15 b=90 c=75 O=1800 A=? H=?
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?
Thank you for this. <3
sir is it possible that only the opposite side is given with an angle of 90
deg.?
Actually helped me a lot with GCSE mock exam … Thanks! 🙂
getting stoned on maths wrap
(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!!
Thankyou so much 🙂
nice beginning
🙂
Great video!
Thank you so much Simon very helpful.
Thank you, helped me!
*students
do you want a job?
– De La Salle High School
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
Thanks Simon
its hypotenuse
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!
thank you so much!
Good explanation, bad audio. Please fix.
thanks really helped alot
thank you soo much
Thank you very much for this tutorial sir . It’s very helpful especially
for my upcoming finals 😛
Great video man 😛
keep it up!
Thank u so much!!! U saved me!!!!!
Thank you for your great explanation. This really helped me out a lot!
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Visit https://www.3minutemaths.co.uk for real maths, tips and techniques.
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 ?
what formula should I do if its given me the angle and the opposite instead
off the hypotenuse ??
Thanks, wouldn’t have done my math project without you :-).
thanks again
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
That’s great – thanks for letting me know 🙂
I struggled so much with this but you helped me so thank you 🙂
Glad to help 🙂
Keep working through questions and you’ll be fine. All best S
oh my god the complication but i’m gonna try my best. thank you 🙂
(T-T) thank you so much!
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
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I did 10 times sin(40) and I got 7.45 what am I doing wrong
such great help ! 🙂
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
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?
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.
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
why did you use sin 40? why not sin 50? that’s the only thing confusing me
Thk You SimonDeacon
th
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 🙂 All best S
what if the hyp is 100 ??
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
If im given one angle, one side and the area, how to do i find the rest? (its a scalene triangle)
Thanks you helped a lot:)
Hi – yes, you need to use the inverse on a calculator to find angles.
do you only inversese sin cos or tan when your finding the angle inside?
Thanks so much.
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.
Denominator / Numerator Sorry flip in words lol.
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
this one i get the formula and the calculation..
Great – thanks for letting me know 🙂
Cheers mate really helped 🙂
thank you so much 🙂
thank you so much 🙂
Thanks this is a really helpful video!!! I get it now!
🙂
That’s great – glad it helped and thanks for letting me know 🙂
Really helpful video!!!!!
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!! :
Hi – latest video – please let me know what you think.. Thanks!