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Study Skills


Trigonometry is the relationship between sides and angles in a right-angled triangle.

Trigonometry is common for a number of trades. It will help you to: 

  • pitch a roof  

  • construct stairs 

  • adjust cutting tools 

  • understand AC theory. 

Working through this page will help you: 

  • understand the basics of trigonometry 

  • label the sides of a triangle 

  • decide which trigonometric ratio to use 

  • use this ratio or formula to help you find the measurement for sides and angles. 

Understanding trigonometry

The video and practice questions are designed to develop skills in identifying triangle sides and for solving trigonometry problems. 


The video below explains the process of trigonometry. Also, it takes you through some examples. After the video, try some review tasks to check your understanding.  


Now, you know how to label each side, review the formulas below. Here is a copy for you to download and keep:


three boxes with formulas

The next task checks your knowledge of the formulas above and your knowledge of side names. We will use Sine for our example.  

Hint: You only need to look at one box.


Using a calculator

After you know which formula to use and any sides or angles, you need to know how to use your calculator to avoid mistakes. Every calculator functions differently to each other. Look at the example below. Is your calculator similar or different? 

Calculator showing the sin, cos, tan and shift buttons.


Look at the example below and follow the steps: 

  • First, label the sides. 

  • Second, work out which formula you will use. 

  • Third, follow the keystrokes to put the equation into your calculator. 

Note: The keystroke is always the same for finding a side length. You just need to substitute sin/cos and tan. 

Question:  What is the length of side A? 


What information do we know? 

100mm is opposite our angle (30°). 
Side A is the hypotenuse.  

So, looking at the formulas, we know we will be using sine and this formula.  

Hypotenuse = Opposite / Sin 0 

Below is the key stroke you need for most calculators. Make sure your calculator is set to DEG

calculator buttons

Now, with your calculator try this key stroke. Your answer should be 200 mm. 

Try it yourself

Now, have a go at these questions. They become more challenging as you work through them. 

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