In these triangles, the small case letters are the sides and the capital equivalents to those letters represent the angles directly opposite them.

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__The Sine Rule__

If, in a question, you are asked to find an angle in a triangle, and you are given

**two sides and another angle**, you need to use the sine rule for**angles**.
Let's imagine that you are given a question like this and you have to find the angle:

Use the first diagram and label the sides and their corresponding angles. Here the missing angle would be A and 7cm would be

*a*, as that is the side opposite the missing angle. 81° would be B, meaning that 18cm would be*b*.
Putting these values in the formula shows us that:

If you are asked to find a missing side in a triangle with

**two angles and one side**, you have to use the sine rule for

**sides**, as illustrated below.

The method used here is similar to the method illustrated above.

###
__The Cosine Rule__

If you are given a question where you have to find the missing side given

**three sides**, you would have to use the cosine rule for**angles**.
Let's imagine you are given a question like this where you had to find the angle:

If the missing angle is A, then 9cm would be

*a*. 10cm would then be*b*and 11cm would then be*c*.
Putting these values in the formula shows us that:

If you are asked to find a

**missing side**with**two sides and an angle**, you would have to use the cosine rule of**sides**.###
__The Area of a Triangle__

If you have an angle and two sides in a triangle and you are asked to find the area, you have to use this formula:

*b*is 10cm and

*c*is 11cm.

Putting these values in the formula gives us:

good

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