The Sine Rule

small Applying the trigonometric ratios to a general triangle.

$${h = b \cdot \sin{\alpha}}$$

and

$${h = a \cdot \sin{\beta}}$$

Equating the two equations:

$${a \cdot \sin{\beta} = b \cdot \sin{\alpha}}$$

Rearranging the equations

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

Similarly, you can show that

$${\frac{a}{\sin{\alpha}} = \frac{c}{\sin{\gamma}}}$$

and

$${\frac{b}{\sin{\beta}} = \frac{c}{\sin{\gamma}}}$$

the sine rule

$${\frac{a}{\sin{\alpha}} = \frac{b}{\sin{\beta}} = \frac{c}{\sin{\gamma}}}$$

or

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

applications

Aufgabe 60 and 61 on Aufgabenfuchs

CIMT - exercises (same as on cosine rule page)


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