SOHCAHTOA and Other Problem Solving

I feel like recently I’ve been doing a whole lot of waiting. Whether it be waiting for a train, an appointment, a person or an event… And they’re just the more tangible sorts of waiting. There are also periods of prolonged waiting, where I find myself waiting for something I’m not sure I’m ready to confront, wanting to do, or even waiting for an unknown to eventuate and present itself with new questions to respond to. I might not be actually anticipating anything, but I might be longing. What these situations have in common is that in each one, I am generally passive, a bystander, looking on to something I cannot control or have an impact upon.

Waiting can provoke great emotions or at times, leave one feeling quite numb. Waiting can be anxiety-provoking, tormenting and frustrating, and it can also damn well boring. Sitting in a doctors’ waiting room, long after the time of your appointment might seem reasonable on one day, but on another, you might feel personally targeted or forgotten. Sure, it’s likely that in these games of waiting, only time will suffice. You will eventually be seen, heard or attended to. You come to terms with the fact that sometimes, things don’t go exactly according to plan, run by the schedule or as you’d hoped. While all this is both obvious and simple to say, I know putting yourself in or coming to a relaxed, accepting state in the moment can be far from easy.

Then there are the more complex waiting experiences, where we feel like we’re endlessly on edge, we’re awaiting a response, or on the action of another, and times when passivity is all we can seem to manage. To quote John Mayer, “We keep on waiting / waiting on the world to change”.

This evening I found myself staring at a painting hanging on an office wall. I can’t recall much of the detail except that it depicted people moving and clotheslines turning in the wind. And the way the artist had painted the clothes lines was simply two triangles on top of a vertical line, like this:


As I gazed at the clotheslines scattered across the paper, I had my first moment since finishing school where I actually missed and craved the simplicity of a mathematical formula. For in the moment, I wished that all life’s problems could be solved by a mathematical equation. In maths, there is a right and a wrong, and a well-established process of getting from point A to point B. Questions are solved, answered, explained by a (supposedly, and for my purposes here I am willing to state, logical) process.

Equations like SOHCAHTOA: I bloody miss sin, cos and tan. Sure, there were the sine and cosine rules to bare in mind, but everything was formulaic, logical, and thus, approachable.

Basic geometric equations were always my specialty. (Note: they were my only specialty in maths). I knew that when the chapter on geometry came around each year, I could relax a bit, because here were formulas I understood. They made sense to me and their visual nature appealed to my ways of thinking.


For a more in-depth reminder of the beautiful simplicity of SOHCAHTOA, visit the aptly named website Maths Is Fun.

If SOHCAHTOA failed me, maybe the triangle or the puzzle was right-angled. Aha! Bring out my good mate Pythag. Punch in the buttons to your Texas Instrument or even do it by hand, the rule is right in front of you if not already ingrained into your maths-despising right brain/logic-loving left brain.

a2 + b2 = c2 where c is longest side of the triangle, the hypotenuse, and thus the sum of the squares of the two other sides

and consequently, a2 = c2 – b2 or b2 = c2 – a2


At times when I’m facing what feels like a million and one unknowns, I yearn for a proven way to solve for x (or a or b or c).

I miss these rules, these certainties, the knowledge that when confronting a task, you’ll be able to solve it, move through it, tackle it with courage and GET IT RIGHT (give or take a few careless daydreaming errors).

Yes, communicative, geographical, psychosocial and many other technologies are constantly evolving, helping us with direction, providing possible approaches or stances to take when we face a wall of unknown xs and ys.

But, waiting for a change that has to come from within can be the hardest of all. Knowing you have to process, decide and act upon a situation or something within yourself in order to walk an alternative, more fruitful path can be extremely challenging. Some of these changes can take days, weeks and even years to come to terms with and in the meantime, you’re left, Sitting, Waiting, Wishing (proof right there that life inspires art, inspires life).

Unlike this guy, who’s infamously just waiting for a mate, we might fall into an unhelpful state slowly, without really noticing how or why we got there. And as intimidating or impossible it may feel to be, at any stage through this process – upon realisation to denial, from acceptance and then action – it is okay to ask for help.

Consult a textbook, a friend, a relative, or a professional. There may or may not be an applicable formula get you out of this place of stuckness, but there will always be a way forward.

So at times when you feel like your constantly waiting for something external to arrive, change or disappear, know that others have been in a similar position and have found a solution, an answer, a way forward, and some relief. And at the risk of sounding preachy, you have the ability to stop waiting for or relying upon that ‘other’.

Change waiting into translating, contemplating and acting. It might be slow and arduous but you’ll be one step closer to solving for x. And until the next x, y or z comes your way, that is enough.


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