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:
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If we have the angle shown, we label the sides for this angle. Opposite = Hypotenuse = opposite the right angle. Adjacent=a is the remaining side/ We are to calculate
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We choose which formula to use depending on which side we gave got and which side we need to find. In this case we have |
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Example: Now we have |
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Example: Now we have
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Example: We have o and want to find h. We use the formula
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is the side opposite the angle x
is the longest side, always
We use one of the formulae
We use the formula
and want to find
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