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Trigonometric ratios: SOH CAH TOA

Trigonometric ratios: SOH CAH TOA

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Trigonometric ratios: SOH CAH TOA

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Explainer Video

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

​xxx​​
The angle you're focusing on (you will either have to find out the value of xxx​ or use it to find the length of a side)
Hypotenuse
The longest side of the triangle
Opposite
The side opposite the angle labelled xxx​​
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()​​
​sin⁡(x)=oppositehypotenuse\sin(x)=\frac{opposite}{hypotenuse}sin(x)=hypotenuseopposite​​​
SOH
Cosine
​cos⁡()\cos()cos()​​
​cos⁡(x)=adjacenthypotenuse\cos(x)=\frac{adjacent}{hypotenuse}cos(x)=hypotenuseadjacent​​​
CAH
Tangent
​tan⁡()\tan()tan()​​
​tan⁡(x)=oppositeadjacent\tan(x)=\frac{opposite}{adjacent}tan(x)=adjacentopposite​​​
TOA


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


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Length:
Drawing and measuring angles with a protractor

Unit 1

Drawing and measuring angles with a protractor

Constructing triangles

Unit 2

Constructing triangles

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Trigonometric ratios: SOH CAH TOA

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Trigonometric ratios: SOH CAH TOA

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FAQs - Frequently Asked Questions

When do I use these trigonometric ratios?

When you have a right-angled triangle and you have to find out either a length or an angle.

Why do poets use tactile imagery?

Tactile imagery is about the sense of touch. It is an evocative way for poets to explain the way things physically feel in a particular instance within the poem, allowing the reader to gain a better understanding of the poet's scene.

What are the 3 main trigonometric functions?

Sin, cos and tan.

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