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.

**SohCahToa**

S=o/h C=a/h T=o/a

sin

θ= 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 ∴ Tan*θ*, which is equal to the opposite over the adjacent:

*tanθ = opp/adj
*tan

*θ = 10/15*

tan

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.