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Maths: Discovering the wonders of trigonometry

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Maths: Discovering the wonders of trigonometry

The best thing about learning trigonometry and discovering the Sin, Cos and Tan buttons have function beyond writing naughty words on your calculator.

Let’s start with the dictionary

The word “trigonometry” can be separated into two parts: “trigono” (triangle) and “metry” (measure). Simply put, trigometry deals with right triangles – the relationship between the sides and the angles.

Why should I bother learning this?

Let’s pretend you want to measure the height of your house. You can either grab tape measure, climb onto the roof and yo-yo it down… or you can take a step back and use some good old-fashioned mathematics.

All you need is the distance you’re standing from the house and the approximate angle between the distance and the height. We can then visualise a triangle and mathematically determine the height of the house. Using this method, we can measure the height of things such as mountains, which would be a bit harder to measure with tape measure.

Remember this nonsense phrase: SOH CAH TOA

Before we go any further, any teacher will first ask you to write down SOH CAH TOA. This stands for:

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

The formula you will use will depend on which values of the triangle you’ve already been provided with. For example, if you’ve been provided values opposite and adjacent to the angle, you would use Tan.

Okay, moving forward…

Let’s find out the height of the tree above. We have already been provided a measurement of 25° on angle B and 8 metres between B and C. The 8-metre value is adjacent to angle B and the side we’re looking for is opposite angle B, so we know we want the formula which involves opposite and adjacent. Using the SOH CAH TOA chart above, we choose Tan = Opposite/Adjacent.

The next step is to write down the trig ratio:

Tan B = opposite/adjacent

Now, we substitute in the angle we know:

Tan 25° = b/8

Now we move the 8 to the other side by multiplying both sides by 8:

8 x Tan 25° = b

b = 3.7m (rounded to the nearest tenth)

Now we know the tree is 3.7m in height. Ta-da!

 

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