Download Trigonometry in all triangles

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.
B
a
c
C
A
b
Sine rule
a/sinA = b/sinB = c/sinC
or
sinA/a = sinB/b = sinC/c
Cosine rule
a2 = b2 + c2– 2bc cosA
or
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
Area = ½ x 6 x 5 = 15 cm2
5 cm
6 cm
This formula is most useful where the triangle is right-angled or
you know the perpendicular height of the triangle.
Area = ½ ab sinC
7cm
40˚
10cm
Area = ½ x 7 x 9 x sin 40˚ = 20.2 cm2 to (1 dp)
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.