Online Instruction from Mathisfun and Khan Academy

We have already that the sine of an angle can be defined as the side opposite the angle on a *right angle triangle that has hypotenuse length 1*. The cosine is the length of the adjacent side, and the tangent is the length on the tangent as seen in the diagram:

For every other right angled triangle, we see that the scale factor is just the length of the hypotenuse:

Now let’s focus on the side opposite the marked angle, the green side. We see that

or, in general,

Which leads us to the formula:

Similarly, the adjacent side, the red length can be calculated as:

Which leads to the formula

Finally, through examining the triangle made with the tangent line:

We see that in this case, the side opposite the angle divided by the side adjacent gives us :

This leads us to three tidy trig formulae for right angled triangles:

Which leads us to the mnemonic: SOH CAH TOA, used for calculating sides and angles on any right angled triangle.

# Finding a side on a right angled triangle

Use the sine; cosine or tangent ratio to find the side indicated.

Draw the triangle onto paper. Label, and show working clearly.