# Refresh my memory. Geometry
**URL:** https://boards.straightdope.com/t/refresh-my-memory-geometry/489116
**Category:** Factual Questions
**Created:** [March 11, 2009, 7:52pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116 "2009-03-11T19:52:45Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Peanuthead](https://boards.straightdope.com/u/Peanuthead)
#### Post date: [March 11, 2009, 7:52pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/1 "2009-03-11T19:52:45Z")
It’s been a long, long time since high school geometry and to tell the truth I wasn’t that good at it anyway. Now that I’m retired and doing some woodworking I finally realize the teacher was right when she said “you will need to know this later in life”. So here’s my situation:
I have a piece of wood 3/4" thick squared off at the end. Measure in from the end 3/8" and make an angle cut across the face of the board.
I see this as a simple geometry problem of a right triangle 3/4" tall and 3/8" at the base. How do I find the other (non 90 degree) angles?
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### Author:  [@Squink](https://boards.straightdope.com/u/Squink)
#### Post date: [March 11, 2009, 8:02pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/2 "2009-03-11T20:02:48Z")
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite over adjacent.
.75/.375 = 2
inverse tangent = arctan = tan[sup]-1[/sup]
[arctan 2 in degrees](arctan 2 in degrees) = 63.435 degrees
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [March 11, 2009, 8:05pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/3 "2009-03-11T20:05:58Z")
And, in case it needs to be said, the other angle would be 90 - 63.453 = 26.565 degrees (since the three angles add up to 180 degrees).
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### Author:  [@Peanuthead](https://boards.straightdope.com/u/Peanuthead)
#### Post date: [March 11, 2009, 8:09pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/4 "2009-03-11T20:09:53Z")
No wonder I didn’t remember it. So, Squink, does that come from a chart somewhere? (your link doesn’t work)
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### Author:  [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)
#### Post date: [March 11, 2009, 8:10pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/5 "2009-03-11T20:10:22Z")
Not a Geometry problem, but a trigonometry problem. 🙂
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [March 11, 2009, 8:22pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/6 "2009-03-11T20:22:02Z")
> [@](#):
>
> No wonder I didn’t remember it. So, Squink, does that come from a chart somewhere? (your link doesn’t work)
There are tables, but nobody actually uses them any more, since all scientific calculators can do the trig functions, and most people with need for trig functions have a scientific calculator.
**Squink** ’s link was probably supposed to be to [Google Calculator](http://www.google.com/search?hl=en&q=arctan+2+in+degrees&btnG=Google+Search&aq=f&oq=) (I got that link just by putting “arctan 2 in degrees” straight into Google’s search box).
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### Author:  [@Peanuthead](https://boards.straightdope.com/u/Peanuthead)
#### Post date: [March 11, 2009, 8:29pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/7 "2009-03-11T20:29:17Z")
> [@Chronos](#):
>
> There are tables, but nobody actually uses them any more, since all scientific calculators can do the trig functions, and most people with need for trig functions have a scientific calculator.
>
> **Squink** ’s link was probably supposed to be to [Google Calculator](http://www.google.com/search?hl=en&q=arctan+2+in+degrees&btnG=Google+Search&aq=f&oq=) (I got that link just by putting “arctan 2 in degrees” straight into Google’s search box).
Good link. Thanks. Guess it’s time to upgrade my “thank you for joining AARP” calculator. 🙂
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### Author:  [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)
#### Post date: [March 11, 2009, 8:45pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/8 "2009-03-11T20:45:59Z")
Your computer has a calculator. They don’t generally display in scientific mode by default, but it is a menu option (at least in OS X, Fedora Linux, and Win XP).
FWIW,
Rob
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### Author:  [@Squink](https://boards.straightdope.com/u/Squink)
#### Post date: [March 11, 2009, 9:30pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/9 "2009-03-11T21:30:06Z")
> [@Chronos](#):
>
> **Squink** ’s link was probably supposed to be to [Google Calculator](http://www.google.com/search?hl=en&q=arctan+2+in+degrees&btnG=Google+Search&aq=f&oq=) (I got that link just by putting “arctan 2 in degrees” straight into Google’s search box).
Yup, Google calc is _very_ handy for those times you don’t have a scientific calculator lying around.
As far as a chart goes, some teacher back in the mists of time told me “SOH CAH TOA”, and I’ve never been able to forget.
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### Author:  [@Kevbo](https://boards.straightdope.com/u/Kevbo)
#### Post date: [March 11, 2009, 10:44pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/10 "2009-03-11T22:44:17Z")
> [@Squink](#):
>
> sin = opposite/hypotenuse
> cos = adjacent/hypotenuse
> tan = opposite over adjacent.
SOHCAHTOA: Ancient Indian word for pretty much all you need to know about triginometry.
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### Author:  [@KCB615](https://boards.straightdope.com/u/KCB615)
#### Post date: [March 11, 2009, 11:04pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/11 "2009-03-11T23:04:21Z")
Some Old Horse Caught Another Horse Taking Oats Away. Thanks, Mr. Sullivan.
I could never remember how to spell SOHCAHTOA.
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### Author:  [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)
#### Post date: [March 11, 2009, 11:41pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/12 "2009-03-11T23:41:36Z")
> [@KCB615](#):
>
> I could never remember how to spell SOHCAHTOA.
It’s actually kind of a terrible mnemonic, isn’t it? I mean, you could so easily imagine thinking it was spelt SAHCOHTOA instead, for example.
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### Author:  [@Fish](https://boards.straightdope.com/u/Fish)
#### Post date: [March 11, 2009, 11:53pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/13 "2009-03-11T23:53:45Z")
You could make that cut pretty well with geometry. A[sup]2[/sup] + B[sup]2[/sup] = C[sup]2[/sup], right? The hypotenuse face would be 0.835" across (between 13/16 and 27/32).
Knowing the length of the hypotenuse, you can just take a ruler and draw it on to the board to guide your cut.
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [March 11, 2009, 11:57pm UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/14 "2009-03-11T23:57:20Z")
> [@Indistinguishable](#):
>
> It’s actually kind of a terrible mnemonic, isn’t it? I mean, you could so easily imagine thinking it was spelt SAHCOHTOA instead, for example.
Not if you store it in auditory memory (as opposed to visual memory).
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### Author:  [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)
#### Post date: [March 12, 2009, 12:15am UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/15 "2009-03-12T00:15:17Z")
What do you mean? Supposing you store it with the pronunciation I usually hear (“sock-uh-toe-uh”), I could easily imagine being confused as to the particulars of the spelling (given the common father-bother vowel merger).
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [March 12, 2009, 12:20am UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/16 "2009-03-12T00:20:32Z")
> [@Indistinguishable](#):
>
> What do you mean? Supposing you store it with the pronunciation I usually hear (“sock-uh-toe-uh”), I could easily imagine being confused as to the particulars of the spelling (given the common father-bother vowel merger).
I’ve always heard it with the “SOH,” the “CAH,” and the “TOA” pronounced as separate syllables (“TOA” is two syllables). (“SOH, a needle pulling thread. CAH, a note to follow SOH. TOA…”—I guess that one doesn’t fit the song as well.)
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### Author:  [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)
#### Post date: [March 12, 2009, 2:16am UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/17 "2009-03-12T02:16:47Z")
> [@Indistinguishable](#):
>
> What do you mean? Supposing you store it with the pronunciation I usually hear (“sock-uh-toe-uh”), I could easily imagine being confused as to the particulars of the spelling (given the common father-bother vowel merger).
Anyone who learns it as “sock” is learning it wrong. It’s “sew” or “so”.
All Mnemonics are of dubious value. They substitute memorizing something correctly for learning the underlying concepts. Every Good Boy Does Fine is one way for a student of music to remember what the lines on the G staff mean, but it’s much better for the student to understand what’s really going on with musical notation, so that they understand what it shows instinctively, rather than trying to remember it and not confusing it with F - A - C - E or Good Boys Do Fine Always (the bass clef lines). HOMES (the Great Lakes) can be very good (I know someone who still uses it to this day as a 50 year old woman, and she has a cabin on an island in one of the lakes, fer goodness sake!), but if you don’t have any reason to remember that HOMES and the Great Lakes are associated, how good is the mnemonic? :smack:
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### Author:  [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)
#### Post date: [March 12, 2009, 2:59am UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/18 "2009-03-12T02:59:00Z")
I agree with everything you say. That having been said, learning SOHCAHTOA is at least a little different from, say, learning about staff notation. What SOHCAHTOA is used to memorize is not, in itself, something for which there is _any_ deeper underlying concept to understand\*: it’s just a matter of familiarity with what terminology denotes what. There’s no good reason that “sine” couldn’t denote what we currently refer to as cosine or tangent or cosecant or what have you, and so forth; it’s all just the arbitrary caprice of linguistic history. And thus, there is no other way to learn this than by memorization of the standard, since all there is to this is… memorization of the standard.
So, yeah, remembering how to apply the mantra SOHCAHTOA and understanding trigonometry are largely orthogonal; one shouldn’t conflate knowledge of terminological conventions with knowledge of substantial mathematical facts. But if one does want to learn the terminological conventions, it’s not as though there’s any more insightful, “Ah, that’s what’s really going on” way to come to know them than by rote.
My only complaint, then, is that SOHCAHTOA is subpar, even for those purposes, being such an arbitrary, made-up word, rather than something independently memorable and resistant to corruption (such as “HOMES”). Even if one did learn it with the “sew” pronunciation, there’s no great guarantee that one would remember it that way, as evidenced both by Google and by my students on occasion.
\*: Yeah, alright, you could make the slight observation that co-f(x) always denotes f(the complementary angle to x). But this is largely opaque even to mathematicians, only just barely of any use in generally remembering what denotes what, and again just a curiosity of terminology, rather than a significant trigonometric fact.
Actually, as far as musical notation goes, apart from “Each space is separated by a semitone from the neighboring ledger line, in linear order”, what deeper underlying concept is there to grasp?
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### Author:  [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)
#### Post date: [March 12, 2009, 3:05am UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/19 "2009-03-12T03:05:32Z")
Er, replace “semitone” with … not semitone. That was a brainfart moment. What I meant, of course, was one scale step (a generic second), whatever the interval that corresponds to in the key signature. Bleh. Anyway, just out of curiosity, what is the deeper underlying concept which is elided by EGBDF mnemonics?
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### Author:  [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)
#### Post date: [March 12, 2009, 11:15am UTC](https://boards.straightdope.com/t/refresh-my-memory-geometry/489116/20 "2009-03-12T11:15:30Z")
Actually, you are a little incorrect about sine, cosine and especially tangent. The function we call “tangent” derives directly from the concept of a tangent to a circle, just as the function we call “secant” derives from a secant. So it is possible, by teaching the concept using the unit circle to give them a way to understand trigonometric functions without having to have them simply memorize a series of apparently arbitrary relationships. Which is how _I_ avoid worrying about SOHCAHTOA (except for those who insist upon some such device, and can’t get by without it). 🙂
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