Trigonometry and Right Angled Triangles – Finding a Side

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There are three basic formulae, involving the ratio of the lengths of the sides. Given a right angled triangle, we first label the sides for the angle we have:

If we have the angle shown, we label

the sides for this angle.

Opposite =is the side opposite the angle x

Hypotenuse =is the longest side, always

opposite the right angle.

Adjacent=a is the remaining side/

We are to calculateWe use one of the formulae

We choose which formula to use depending on which side we gave got and which side we need to find. In this case we haveand need to findso we use the formula 

Example:

Now we haveand want to findWe use the

formula

Example:

Now we haveand want to findWe use the formula

Example:

We have o and want to find h. We use the formula

It is important to realise the difference between the formulae

 and 

For the first we write but for the second we actually work out 

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