Trigonometry and Right Angled Triangles – Finding an Angle

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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 choose or have been given:

Given we have chosen the anglewe label the sides for this angle.

Opposite = is the side opposite the angle 

Hypotenuse =is the longest side, always opposite the right angle.

We are to calculateWe use one of the formulae

We choose which formula to use depending on which sides we gave got. In this case we have  so we use the formula 

Now we solve 

Example:

Now we haveandWe use the formula

We solve 

Example:

Now we haveandWe use the formula

We solve 

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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