Home > Trigonometry > Law of sines & Law of cosines

## Law of sines & Law of cosines

Proovement of law of sines and cosines.

Law of sines

$b \cdot sin \alpha = h , a \cdot sin \beta = h \Rightarrow$

$\Rightarrow b \cdot sin \alpha = a \cdot \sin \beta \Rightarrow$

$\Rightarrow \frac{ b }{ sin \beta } = \frac{ a }{ sin \alpha }$

Law of cosines

$BH = a \cdot cos \beta , AH = c - a \cdot cos \beta$

$h^2 = a^2 - a^2 \cdot cos^2 \beta \: and \: h^2 = b^2 - c^2 - a^2 \cdot cos^2 \beta + 2ac \cdot cos \beta$

$b^2 = a^2 + c^2 - 2ac \cdot cos \beta$

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