Question

select the correct choice that completes the sentence below.
for a triangle with sides a, b, c, and opposite angles a, b, c, the law of sines states that
\\( \frac { \sin a } { b } = \frac { \sin b } { a } = \frac { \sin c } { c } \\)
\\( \frac { \sin a } { b } = \frac { \sin b } { c } = \frac { \sin c } { a } \\)
\\( \frac { \sin a } { a } = \frac { \sin b } { b } = \frac { \sin c } { c } \\)
\\( \frac { \sin a } { c } = \frac { \sin b } { b } = \frac { \sin c } { a } \\)
\\( \frac { \sin a } { c } = \frac { \sin b } { a } = \frac { \sin c } { b } \\)
\\( \frac { \sin a } { a } = \frac { \sin b } { c } = \frac { \sin c } { b } \\)

Explanation:

The Law of Sines states that in any triangle, the ratio of the sine of an angle to the length of its opposite side is constant. That is, for a triangle with sides \(a\), \(b\), \(c\) and opposite angles \(A\), \(B\), \(C\) respectively, we have \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\).

Answer:

\(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\) (the third option in the given choices)