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marklucas856

2019. július 4. 11:59

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Hi, just wondering if someone can clear something up for me?

Solving for a side - law of sines I have the following equation:
SinB / b = SinA / a
I multiply both by ‘b’ which leads me to:
SinB = SinA / a • b

However in hints it says I should have:
SinB = b/a SinA

I’m hoping someone could help me understand how they come to this in the equation.
Thanks in advance.

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Forgotten

2019. július 4. 12:09
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Hozzászólás-műveletek Permalink
SinA / a * b = b * SinA / a = b / a * SinA = b/a SinA

They omitted the multiplication operator here.

If you want to understand the formula. Do a geometric proof of it.
Forgotten

2019. július 4. 12:38
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Hozzászólás-műveletek Permalink
Algebraically you can do a simple proof as follows.

Let h be the height of a triangle ABC perpendicular to the side AB.

Let a, b, c be BC, AC, AB respectively.

It follows that

sin A = h/b and sin B = h/a.

h = h <=>

<=> b/b * h = a/a * h <=>

<=> b * h/b = a * h/a <=>

<=> b * sin A = a * sin B <=>

<=> 1 / (ab) * b * sin A = 1 / (ab) * a * sin B <=>

<=> b/(ab) * sin A = a/(ab) * sin B <=>

<=> 1/a * sin A = 1/b * sin B <=>

<=> (sin A) / a = (sin B) / b

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