Usually, Trigonometry is used to deal with right-angled triangles. Trigonometry helps to find out the sides and angles using the relationship between them. Both the Sine and Cosine rules apply to any triangle - not just right-angled triangles.
- In right angled triangles, the side next to the angle you are using is called the 'adjacent', the side opposite, is called that. The longest side is called the hypotenuse.
- For the sine rule, the cosine rule and areas of triangles, the sides are labelled a,b and c and the angles opposite a,b and c are labelled A, B and C.
$ sin(x)=opposite/hypotenuse $
$ cos(x)=adjacent/hypotenuse $
$ tan(x)=opposite/adjacent $
The sine, cosine, and tangents can be remembered by this rhyme: Some old hag came and had tea one afternoon (sine: opposite/hypotenuse, cosine: adjacent/hypotenuse, tangent: opposite/adjacent).
Another good memory aid is SOH, CAH, TOA. They are abbreviations for [sine=opposite/hypotenuse], [cos=adjacent/hypotenuse] and [tan=opposite/adjacent].
The Sine RuleEdit
The Cosine RuleEdit
$ a^2=b^2 + c^2 -2bccos(A) $