Trigonometry in all triangles
The sine rule and cosine rule can be used with any triangle, including right-angled triangles.
You should know how to use the sine rule and the cosine rule.
You should know when to apply the sine rule and when to apply the cosine rule.
a/sinA = b/sinB = c/sinC
sinA/a = sinB/b = sinC/c
a2 = b2 + c2 – 2bc cosA
cosA = (b2 + c2 – a2)/2bc
The Formulae Booklet in the exams will only give the cosine rule in the first form (for finding a side length), so you need to be able to rearrange it into the second form (for finding an angle).
Area of a triangle
Area = ½ base x height
This formula is most useful where the triangle is right-angled or you know the perpendicular height of the triangle.
Area = ½ ab sinC
This formula for the area of a triangle can be used if you know the lengths of two sides and the size of the angle between them.
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