What is the Law of Sines?

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What is the Law of Sines?

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Answer 1 · 2015-01-30T18:36:26

First of all it is useful to say the notation in a triangle:

Opposite at the side $a$ $a$ the angle is called $A$ $A$ ,
Opposite at the side $b$ $b$ the angle is called $B$ $B$ ,
Opposite at the side $c$ $c$ the angle is called $C$ $C$ .

So, the Sinus Law can be written:

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a/sinA=b/sinB=c/sinC$ .

This Law is useful in all the cases SSA and NOT in the case SAS, in which the Law of Cosinus has to be used.

E.G.: we know $a, b, A$ $a,b,A$ , then:

$sin B = sin A \cdot \frac{b}{a}$ $sinB=sinA*b/a$ and so $B$ $B$ is known;

$C=180°-A-B$ and so $C$ is known;

$c=sinC/sinB*b$

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What is the Law of Sines?

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