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Sine & Cosine Rules (Edexcel IGCSE Maths)
Revision Note
Sine Rule
What is the sine rule?
- The sine rule allows us to find missing side lengths or angles in non-right-angled triangles
- It states that for any triangle with angles A, B and C
-
- Where
- a is the side opposite angle A
- b is the side opposite angle B
- c is the side opposite angle C
- Where
- You not need to remember it
- Sin 90° = 1 so if one of the angles is 90° this becomes SOH from SOHCAHTOA
How can we use the sine rule to find missing side lengths or angles?
- The sine rule can be used when you have any opposite pairs of sides and angles
- Always start by labelling your triangle with the angles and sides
- Remember the sides with the lower-case letters are opposite the angles with the equivalent upper-case letters
- Use the formula in the formula booklet to find the length of a side
- To find a missing angle you can rearrange the formula and use the form
- Substitute the values you have into the formula and solve
- This will always give you an acute angle
- If you know the angle is obtuse then subtract this value from 180
Examiner Tip
- Remember to check that your calculator is in degrees mode!
Worked example
The following diagram shows triangle ABC. , , . The angle is acute.
Use the sine rule to calculate the value of:
i)
,
ii)
.
Cosine Rule
What is the cosine rule?
- The cosine rule allows us to find missing side lengths or angles in non-right-angled triangles
- It states that for any triangle
;
-
- Where
- a is the side opposite angle A
- b and c are the other two sides
- Where
- You are not given either formula
- You could memorise both of them
- Or you could memorise the first one and rearrange it each time you use it
- Cos 90° = 0 so if A = 90° this becomes Pythagoras’ Theorem
How can we use the cosine rule to find missing side lengths or angles?
- The cosine rule can be used when you have two sides and the angle between them or all three sides
- Always start by labelling your triangle with the angles and sides
- Remember the sides with the lower-case letters are opposite the angles with the equivalent upper-case letters
- Use the formula to find an unknown side
- Use the formula to find an unknown angle
- A is the angle between sides b and c
- Substitute the values you have into the formula and solve
Examiner Tip
- Remember to check that your calculator is in degrees mode!
Worked example
The following diagram shows triangle . , , .
Calculate the value of angle .
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