Sine Formula
What is the sine formula?
- The sine formula allows us to find missing side lengths or angles in non-right-angled triangles
- It is also known as the sine rule
- It states that for any triangle with angles A, B and C
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- a is the side opposite angle A
- b is the side opposite angle B
- c is the side opposite angle C
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- This formula is not on the exam formula sheet, so you need to remember it
- Remember that sin 90° = 1
- So if one of the angles is 90° this becomes SOH from SOHCAHTOA
How can I use the sine formula to find missing side lengths or angles?
- The sine formula 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
- Remember
- Use the formula as given above to find the length of a side
- To find a missing angle it's easier to 'flip' the formula
- 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
Exam Tip
- Remember to check that your calculator is in the correct angle mode (degrees or radians)!
Worked example
The following diagram shows triangle . , , and angle . It is also given that angle is acute.