# How do you use trigonometry to work out angles and lengths of sides in a right angle triangle

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Using the trigonometric(trig) ratios of cosine, sine and tangent we can work out side lengths and angles.

Within a right angle triangle of we are given a side lenght and a angle other than the right angle we can work out either of the other two sides.

Each side is given a name depending on how it relates to the given angle. The longest side on the triangle is called the hypotenuse. The side which is touching the angle but is not the hypotenuse is called the adjacent. The other side the one which is not touching the given angle and is also not the hypotenuse is called the opposite as it is opposite the angle.

Depending on which side we are given and which we want to work out depends which trig ratios we use.

The phrase SOH CAH TOA is an easy way to remember whihc goes with which. So if we look at SOA the S is for sine and the sides are opposite and hypotenuse. So if the sides involved aare those two we use sine. CAH and TOA follow the same order. For these three ratios this means tthat the sine of an angle is equal to the length of the opposite divided by the length of the hypotenuse. For the other two replacing the correct parts.

So to work out a length we can put out known likely into the equation then rearrange it to solve for the unknown side. To get the sine of an angle on your calculator there will be a button with "sin". This should make a "sin(" appears on the screen. Inside the brackets you put the angle. This will give a number most likely with alot of decimal places it is best to carry this using your calculator and round your final answer to three significant figures.

​To calculate angles when given two sides is slightly more complex and requires the use of inverse trig rations. These are written as sin-1 cco-11 and tan-1

We follow the same rules for idenroff in which ratio we use. We fillook in what we know . This will give us the trig ratio of a  unknown angle is equal to a number. To calculate the angle we use the inverse trig ratio. For example if we have sin of an unknown  we use sin-1. We take the inverse  ratio of the number we do this by pressing shift then the normal ratio. It should display "sin-1(" wwepputwe put oojrr number inside the bracket and this gives us the angle  which we then round to three significant figures.

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