Can you use trigonometric functions for any kind of triangle?

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Can you use trigonometric functions for any kind of triangle?

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Answer 1 · 2015-03-26T03:49:29

It depends on what you mean by "use trigonometric functions".

The Law of Sines tells us that for any triangle: labelled with
$a$ $a$ = length of the side opposite angle $A$ $A$
$b$ $b$ = length of the side opposite angle $B$ $B$
$c$ $c$ = length of the side opposite angle $C$ $C$
we have:

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

(So also, by algebra: $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a/sinA = b/sinB = c/sinC$ )

The Law of Cosines generalizes the Pythagorean Theorem.
It says that in any triangle labelled as above, we have:
$c^{2} = a^{2} + b^{2} - 2 a b cos C$ $c^2=a^2+b^2-2ab cosC$
$b^{2} = a^{2} + c^{2} - 2 a c cos B$ $b^2=a^2+c^2-2ac cosB$
$a^{2} = b^{2} + c^{2} - 2 b c cos A$ $a^2=b^2+c^2-2bc cosA$

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Can you use trigonometric functions for any kind of triangle?

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