We often come across the mnemonic SohCahToa when we first encounter trigonometry. I’m not a huge fan, but it has its uses. So we will take a short look at it here. The ratios of the sine, cosine, and tangent of θ to the adjacent, opposite, and hypotenuse form a general and basic rule of trigonometry.
S=o/h C=a/h T=o/a
sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
Where θ – or ‘theta’ – is the measure of the unknown angle.
Lets show how this works:
If we have a right angled triangle where we know the value of at least two of its side we can use trigonometry to calculate the measure of the angle:
In the above right triangle we see that we have the measure of two sides and an unknown angle, θ. We can label these known lines as the adjacent (because it is beside the relevant angle) and the opposite (because it is facing the relevant angle).
When we look at SohCahToa we are of course looking for the section that includes both ‘o‘ and ‘a.’ That is ‘Toa’ and ∴ Tanθ, which is equal to the opposite over the adjacent:
tanθ = opp/adj
tanθ = 10/15
tan-1 (10/15) = 33.69°
We can also work this from a known angle and a known line measurement to discover the measurement of the other lines. Using the same example, if we know the relevant angle is 33.69° and that the adjacent line is 15 we can do this:
opp = tanθ × adj
opp = tan33.69 × 15
∴ 15tan33.69 = opp
15tan(33.69) = 9.999 ∨ 10
As you can see this is quite a simple tool. It is well worth getting to know and practising often if you are doing your exams – or just a nerd like me – because this one will come up in every single maths exam in one form or another. If you have any questions just leave them in the Thoughts and Questions section below.