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Geometry in two dimensions
Right angled Trigonometry
Worked Examples
The Sine Rule
Sine Rule
or the inverse
Area of triangle
The Cosine Rule
Given the triangle ABC as shown

Useful rules:
The largest angle is opposite the largest side, also the smallest angle is opposite the shortest side
The two right angled triangles with sides in the ratio 3:4:5 and 5:12:13


MATH STUDIES
Geometry and Trigonometry
Nonright angled Trigonometry: The Sine Rule and the Cosine Rule
The Sine Rule and the Cosine Rule : Worked Example
Given triangle ABC where AB = 5cm and BC = 7cm and angle C = 40° Find
Angle A
AC
Area of triangle ABC
First sketch the triangle with the information given
(Diagram not to scale)
Using the sine rule:
To find AC we can use the sine or cosine rule as we now no that angle B = 180  40 64.1 =75.9°
Using the cosine rule: AC^{2} = AB^{2} + BC^{2}  2 x AB x BC cos B
Hence AC^{2} = 5^{2} + 7^{2}  2 x 5 x 7 cos 75.9
AC = 7.55 cm
(correct to 3 significant figures)
Using Sine rule
(there is a slight difference in values)
Area triangle ABC
Notes:
Try and use values given as much as possible to ensure greater accuracy in answers
Do the calculation all in one step on the calculator to avoid rounding errors.
Remember brackets on the calculator. Example sin40 should be entered as sin(40)

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