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Trigonometric ratios: SOH CAH TOA

Trigonometric ratios: SOH CAH TOA

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Proportion


Ratio


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Tutor: Bilal

Summary

Trigonometric ratios: SOH CAH TOA

In a nutshell

Trigonometric ratios allow you to find a length or angle of a right-angled triangle. To do so, you need to know how to label one.


Labelling a triangle


Label

Meaning

xx​​
The angle you're focusing on (you will either have to find out the value of xx​ or use it to find the length of a side)
Hypotenuse
The longest side of the triangle
Opposite
The side opposite the angle labelled xx​​
Adjacent
The side next to the labelled angle that isn't the hypotenuse


Maths; Trigonometry; KS3 Year 7; Trigonometric ratios: SOH CAH TOA



The three trigonometric functions

These are the 3 main functions and their ratios:


Function name

Found on your calculator as

Corresponding ratio

Simplified version

Sine
sin()\sin()​​
sin(x)=oppositehypotenuse\sin(x)=\frac{opposite}{hypotenuse}​​
SOH
Cosine
cos()\cos()​​
cos(x)=adjacenthypotenuse\cos(x)=\frac{adjacent}{hypotenuse}​​
CAH
Tangent
tan()\tan()​​
tan(x)=oppositeadjacent\tan(x)=\frac{opposite}{adjacent}​​
TOA


Note: It is common and easy to just remember these three as SOH CAH TOA.


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