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[h] SL 3.2 Use of sine, cosine and tangent ratios
[q] Trigonometric ratios
[a] One may notice that when you have a right-angled triangle and one other known angle, it doesn’t matter what ‘size’ the triangle is, the ratios between the three sides remain constant. The ratios can be calculated with trigonometric functions sine, cosine and tangent (sin, cos and tan).
Each one of these relates to a ratio of pair of side.
\(sin\theta= \frac{Opp}{Hyp}\) : SOH
\(cos\theta= \frac{Adj}{Hyp}\) : CAH
\(tan\theta= \frac{Opp}{Adj}\) :TOA
[q] All Triangles
[a] As any traingle can be split into two right-angled traingles, these rules may be extended to let us work with any type of traingle.
If we label a traingle as shown above then, we have three rules namely: Sine Rule, Cosine Rule and Area Rule.
[q] Sine Rule
[a]
For the traingle as shwon above, the Sine Rule is given by: \(\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}\)
[q] Cosine Rule
[a]
For the traingle as shwon above, the Cosine Rule is given by: \(Cos(C) = \frac{a^2+b^2-c^2}{2ab}\)
[q] Area Rule
[a]
For the traingle as shwon above, the Area Rule is given by: \(Area = \frac{1}{2}×ab×SinC\)
[x] Exit text
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