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Trigonometry is a method to calculate the sides and angles of a right-angled triangle.

To use trigonometry, the first thing we need to do is label the sides. each side has a specific name:

  • Hypotenuse - The longest side (opposite to right angle)

  • Opposite - Opposite the angle that is in the question  

  • Adjacent - the side next to the angle in the question 

The rules:

A useful way to remember these is SOH CAH TOA.

A worked example for calculating a side:

                                                                 Find the length of side 'a'.


First, we can look at what we know about the triangle. 

  • We know the hypotenuse 

  • Angles B and C

Now we see which equation to use.

  • SOH CAH TOA - we know h and need to know a so we use 

  • CAH - 

  • Now we can put in the numbers 

  • Cos(32) = adjacent/12

  • Rearrange to make a the subject 

  • Cos(32) x 12 = a 

  • a = 10.2

Worked example for calculating an angle:

                                                                   Find the size of angle 'X'

First, look at what we know:

  • The length of sides o and a 

  • The size of angle C

Now we can look at our equations. 


  • We will use TOA - 

Now put the numbers in 

  • tan(x) = 3/5

  • tan(x) = 0.6

  • now we need to use the inverse tan button.

  • tan-1(0.6) = 31

  • X = 31