Trigonometry

L.O To be able to find lengths of right angled triangles using SOH-CAH-TOA

This method is used to work out the lengths and angles of right angled triangles when you may not be able to apply Pythagoras to it. Now you will use the sin, cos and tan buttons on your calculator. These tell you how to work out lengths as a ratio of two other lengths using the angle present.

Before even using sin, cos and tan you must be comfortable labelling the different sides of the triangle with respect to the angle.

Always label the hypotenuse the first as it is the most obvious; the longest side.

Adjacent means ‘next to’, so the side next to the angle is labelled Adj.

Then the remaining side is Opp.

Here the angle marked is in a different place so the side reverse a little.

Again label the hypotenuse first, then the opposite and adjacent sides will be more clear.

This is the standard triangle we started with in Pythagoras.

The angle marked is a right angle so we use the standard sides we learnt initially.

Now applying the functions:

These are the rules that you will need to learn when tackling problems

Sin(x) = Opposite ∕ Hypotenuse

Cos(x) = Adjacent ∕ Hypotenuse

Tan(x) = Opposite ∕ Adjacent

This will all become clearer when we try some problems… don’t worry!

Example 1:

Firstly label the length and the unknown side with A,H or O.Now using your formulas which function uses the sides Hyp and Adjacent ?