 and Pythagoras to find missing size and missing angles in right-angled triangles. But triangles don't always have a right angle, so we need a plan B. For any triangle we have two special formulae, the sine rule and the cosine rule. You probably already guessed the sine rule involves sine and the cosine rule involves cos. In this video we're going to look at how to use the sine rule to find missing sides or missing angles. As there's no right angle we can't use Sokotoa. We use the sine rule. It can be written like this or like this. The little a, b and c represent the sides and the capital a, b and c are the angles. Notice how angle a is opposite side a. Angle b is opposite side b and angle c is opposite side c. This is really important. The formulae is written in two different ways because this way is best for finding missing sides and this way is best for finding missing angles. So let's jump straight in and look at an example. So start by labelling the sides as a and b and the angles as capital a and capital b. So let's call 1.5 centimeters side a. 55 degrees must be angle a and so then 80 degrees is angle b which means the missing side x is this will be. We need to find a missing side so we'll use this version of the formula. So we just substitute in the numbers and we get 1.5 divided by sine 55 equals b divided by sine 80. So to get b on its own we do some simple rearranging by multiplying both sides by sine 80 and then these ones cancel each other out and we're left with b equals 1.5 divided by sine 55 multiplied by sine 80 which we can enter into our calculator. And this gives us 1.8 meters. So let's now have a look at an example where we're trying to find a missing angle. So we need to use this version of the sine rule the missing angle version. Give this one a go yourself. Pause the video, work out the answer and click play when you're ready to check. Did you get 87.5 degrees? If you did and you want to skip the explanation click here otherwise let's go through it together. So we start by labeling the sides and angles with a's and b's so I'm going to label 1.8 meters as a so therefore 46 degrees must be angle a so then 2.5 is side b and the missing angle x is capital B. Again just substitute the numbers into the formula and we get sine 46 divided by 1.8 equals sine x divided by 2.5. A little bit of rearranging so multiply both sides by 2.5 and they cancel out on this side and we get 2.5 multiplied by sine 46 divided by 1.8 which we can enter into our calculator. So then sine x equals 0.999 and so on. Remember to get x on its own we must use inverse sine. In our calculators type in sine to minus 1 brackets 0.999 etc close brackets enter so that gives us 87.5 degrees and that is all you need to be able to use a sine rule. You can find a missing side using this version and a missing angle using this version. Although there are three parts we only ever use two of them so I just ignore the C and the sine C and stick to A's and B's. In the next video we're going to look at when you can and when you cannot use a sine rule and how the cosine rule works when the sine rule doesn't.