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Sine Rule

Introduction

Sine rule is another trigonometry rule that allows you to find missing angles and sides of certain triangles (in some cases you will have to use cosine rule). On the right, you can see the two different types of sine rule. One is for finding missing lengths and the other for finding missing angles. In order to use sine rule, one side and the angle opposite must be known as well as one other length or angle.

Finding Lengths Using Sine Rule

To find a missing length of a side in a triangle, we need to use the first formula of the ones above. Start off by labelling the triangle so that the angles are A, B and C and the angles opposite to them are a, b and c. In this case, we are using a and b so we start off by writing down the formula as we have done on the left. Then simply substitute the values from the triangle into the equation. To solve the equation, we simply have to multiply both sides by sin35 so that we end up with ? on one side and all known values on the other. The last step is to use your calculator to solve the equation which will provide you with the missing length.

Finding Angles Using Sine Rule

In order to find a missing angle, you need to flip the formula over (second formula of the ones above). Again, it is necessary to label your triangle accordingly. In this case, we are working with a and c and so we write down the c and the a part of the formula as has been done on the left. The next step is to substitute the values into the formula and then multiply by both sides by 5 in order to have sin? equal to known values (making Sin? the subject of the formula). Now simply use the inverse Sin function on your calculator and insert the fraction with the known values to find the size of the angle. Underneath are some examples.

Examples

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Example 1 In this example, we have used sine rule to find a missing length a. We simply substituted the known values into the equation and then solved it to find the missing length.
Example 2 In this example, we have used Sine rule to find a missing angle C. We have substituted the values into the formula and then solved the equation to find the missing angle.
Example 3 In this example, we have used sine rule to find a missing length c. We simply substituted the known values into the equation and then solved it using a calculator in order to find the missing length.
Example 4 In this example, we have used Sine rule to find a missing angle A. We have substituted the values into the formula and then solved the equation to find the missing angle. We had to use the inverse sine function on our calculator.

Moving on to Cosine Rule

Now that you know how to use sine rule, you should learn about cosine rule which will give you even more possibilities when it comes to finding missing angles and lengths of triangles. Please share this page if you like it or found it helpful!
Cosine Rule 31.0 TRIGONOMETRY 31.1 SIN / COS / TAN 31.3 COSINE RULE
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Chapter 31.2:  Learning Outcomes Students will learn how to find missing angles of non right-angled triangles using sine rule! Students will learn how to find missing sides of non right-angled triangles using sine rule!

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