# Trigonometry

Hi, could you please explain to me what the deal is with SOH CAH TOA in trigonometry?

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davetutors1
21 May 2014
So it all depends which angle you're trying to find.First thing to note is that the SOHCAHTOA rule only works with right-angled triangles.  Here's what everything stands for, so you know what's going on:S='Sin' C='Cos' T='Tan' O='Opposite' A='Adjacent' H='Hypotenuse'So. Let's say you're trying to find the red angle that I've drawn. The hypotenuse is always the longest line; the one opposite the right angle. The 'opposite' is the one opposite the angle you're trying to find, and the 'adjacent' is the one next to the angle you're trying to find.The SOHCAHTOA thing is just a way to remember what you do with the numbers, and which one of sin, cos, or tan to use. 'SOH' means 'Sin= Opposite divided by Hypotenuse'. CAH means 'Cos=Adjacent divided by Hypotenuse', and TOA means 'Tan= Opposite divided by Adjacent'.Which one you use depends on what lengths you are given in the question. Thgis is all very tricky to explain so here;'s an example. You're given a right angled triangle like the one I've drawn, and you're trying to find the red angle. You're told that the opposite line -'O'- is 6cm, and the adjacent line-'A'- is 4.You now know the 'O' and the 'A'. Which out of the 3 SOHCAHTOAs has O and A in it? TOA. So you know to use 'Tan'. The next bit's easy. If the angle you want is 'x', you make an equation:Tanx=6/4Rearrange it...x=InverseTan(6/4)so x=56.3 degrees.Easy. Also, if you have the angle and you need to find one of the lengths, you can just put in the angle where 'x' is, and use 'x' for one of the lengths.I hope this helps, it's really simple once you get the hang of it. Let me know if you want some more help.
alex_armitage
21 May 2014
Ignore the sketch, that's not how it was meant to come out...
alex_armitage
21 May 2014
Your triangle (the one currently at the bottom of the page) has no right angles in it - you will need SIN rule or COS rule (in a typical Maths GCSE question, say).Although there are right angles in the triangle when you chop it in half. This is where the SIN and COS rules come from..
Steve R.
22 May 2014
It seems that if you draw a line based diagram it gets corrupted when you post it.
Steve R.
22 May 2014
Hello! I can tutor on trigonometry. Would like to schedule a class?
joaogabriel
23 May 2014
sohcahtoa-all.png
Carlo P.
24 May 2014
Hey, SOH CAH TOA is a mnemonic to remember trigonometric relations in a right-angled triangle. It is simple enough to help remember, but it takes a while if you'd like to understand WHY these relations work. I'd be happy to help if you would like to schedule a class.
Carlo P.
24 May 2014
SOH CAH TOA refers to the formulae:Sinx=Opposite/HypotenuseCosx =