# Can you use trigonometric functions for any kind of triangle?

Mar 26, 2015

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

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

$\sin \frac{A}{a} = \sin \frac{B}{b} = \sin \frac{C}{c}$

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

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