Trigonometry

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

Answers
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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
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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 = 
kubajasko
26 May 2014
SOH CAH TOA refers to the formulae:Sinx  = Opposite/HypotenuseCosx = Adjacent/HypotenuseTanx = Opposite/Adjacent Where x is the angle in question in degrees and the lengths are the sides of the triangle in respect to that angle.Can only provide a limited explanation in words but hope this helps :)
kubajasko
26 May 2014
first draw a right angled triangle. The long side is called the hypotenuse or H. Draw in the angle you want to know. The side that touches that angle you want to find is called the adjacent side or A. The last side that doesn't touch the angle is called the Opposite side or O. All that remains is to use the right one of these:  SOH CAH TOA, to find the angle. You need a calculator with sin, cos, and tan on it.  Next to choose which one of SOH or CAH or TOA, you need lengths of two sides. So if you have the opposite length and the hypotenuse, you have the O and the H, so you should choose TOA. T stands for Tan on your calculator. You then times the O and the H and then press Tan on your calculator. That will give you the angle side you are trying to find.  
jonathanwinter
28 May 2014
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