reciprocal form Of law of sines . question

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• Jan 24th 2014, 03:47 AM
Riazy
reciprocal form Of law of sines . question
Hello i am a bit confused when it comes to this law.

How do i know when the reciprocal form is to be used
And how do i know when its not to be used?

If anyone could make an example.

Thanks
• Jan 24th 2014, 04:09 AM
romsek
Re: reciprocal form Of law of sines . question
Quote:

Originally Posted by Riazy
Hello i am a bit confused when it comes to this law.

How do i know when the reciprocal form is to be used
And how do i know when its not to be used?

If anyone could make an example.

Thanks

The two forms are equivalent. The non-reciprocal form nicely equals the diameter of the circle circumscribing the triangle.

I can see using one or the other to try and keep very small numbers out of the denominator when doing things numerically.
• Jan 24th 2014, 06:52 AM
Soroban
Re: reciprocal form Of law of sines . question
Hello, Riazy!

It really doesn't matter which form you use.

. . $\displaystyle \frac{a}{\sin A} \,=\,\frac{b}{\sin B}\,=\,\frac{c}{\sin C}\,\text{ is equivalent to }\,\frac{\sin A}{a} \,=\,\frac{\sin B}{b} \,=\,\frac{\sin C}{c}$

However, depending on what you are seeking,
. . there is a more convenient choice.

Example: .$\displaystyle b = 7,\:A = 50^o,\:B = 60^o.\;\text{ Find }a.$

Since we want $\displaystyle a$, I would choose the form with $\displaystyle a$ on top.

. . $\displaystyle \frac{a}{\sin A} \,=\,\frac{b}{\sin B} \quad\Rightarrow\quad \frac{a}{\sin50^o} \,=\,\frac{7}{\sin60^o} \quad\Rightarrow\quad a \,=\,\frac{7\sin50^o}{\sin60^o}\;\text{ . . . etc.}$