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Geometry in two dimensions
Non-right angled Trigonometry: The Sine Rule and the Cosine Rule
Worked Examples

 

Notes:

  1. Side a is opposite angle A, side b opposite angle B and side c opposite angle C

  2. Side AB is the hypotenuse.

  3. 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

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Geometry and Trigonometry

Right angled Trigonometry

 

triangle1

  1. Pythagoras's Theorem : (The square on the hypotenuse is equal to the sum of the squares on the other two sides)

    a2+b2=c2  or  AB2 = AC2 + BC2

  2. SOHCAHTOA

    equation1

    equation2

    equation3

  3. Area of triangle ABC  equation4

 

Example:

triangle2

Given AB = 8cm and BC = 5cm  Find

  1. AC

  2. Angle C

  3. Area of triangle ABC

 

Working:

  1. From Pythagoras we know AB2 = AC2 + BC2

    Hence  82 = AC2 + 52

    AC2 = 82 - 52

    equation6 units. This is the exact answer or 6.24 units to 3 significant figures

  2. equation7

  3. Area of triangle ABC  equation8

 

Note: Not all triangles have a right angle, for non-right angled triangles we have other rules

 

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