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Geometry in two dimensions
Nonright angled Trigonometry: The Sine Rule and the Cosine Rule
Worked Examples
Notes:
Side a is opposite angle A, side b opposite angle B and side c opposite angle C
Side AB is the hypotenuse.
For angle A side BC is the opposite and AC the adjacent
SOHCAHTOA
SOH...
Sine = Opposite /
Hypotenuse
...CAH...
Cosine = Adjacent / Hypotenuse
...TOA
Tangent = Opposite /
Adjacent


MATH STUDIES
Geometry and Trigonometry
Right angled Trigonometry
Pythagoras's Theorem : (The square on the hypotenuse is equal to the sum of the squares on the other two sides)
a^{2}+b^{2}=c^{2} or AB^{2} = AC^{2} + BC^{2}
SOHCAHTOA
Area of triangle ABC
Example:
Given AB = 8cm and BC = 5cm Find
AC
Angle C
Area of triangle ABC
Working:
From Pythagoras we know AB^{2} = AC^{2} + BC^{2}
Hence 8^{2} = AC^{2} + 5^{2}
AC^{2} = 8^{2}  5^{2}
units. This
is the exact answer or 6.24 units to 3 significant figures
Area of triangle ABC
Note: Not all triangles have a right angle, for nonright angled triangles we have other rules
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