When do I use a cosine rule over a sine rule?

Both the sine and the consine rule applies to any triangle, you do not necessary need a right angle! 

You can usually use the cosine rule when you are given two sides and the included angle (SAS) or when you are given three sides and want to work out an angle (SSS)

In order to use the sine rule, you need to know either two angles and a side (ASA) or two sides and a non-included angle (SSA).

- Use the sine rule when a problem involves two sides and two angles

  • Use the cosine rule when a problem involves three sides and one angle

The cosine equation:
a= b2 + c2 - 2bccos (A)
(version given on formula sheet to find missing side)
cos (A) = (b+ c2 - a2) / 2bc
(use this version for finding a missing angle)

The sine equation:
a / sinA = b / sinB = c / sinC (use to find the missing side)
sinA / a = sinB / b = sinC / c (use to find the missing angle)

Key points to remember:

Sine Rule:

  • As you label the triangle, each side has the same letter as its opposite angle!
  • If you are wanting to find the angle in the equation remember to use the sin-1 function on your calculator.
  • The greater the length is the greater is the opposite angle!

Cosine Rule:

  • Remeber to use BIDMAS when you work out the value on the right hand side for finding the missing side, hence put brackets around the (2bccos (A) ).

Answered by Jessica F. Maths tutor


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