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# triangle trig

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Jul 26, 2020

#1
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Law of sines

sin 70o  / 5.7 = sin xo / 5       solve for 'x'

Jul 26, 2020
#3
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TheLovely1  Jul 26, 2020
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Hello, Guest!~

I'm going to elaborate on Electric Pavlov's excellent answer.

So, basically, the Law of Sines says that, according to Khanacademy, a side labeled, "A" over the sine * opposite of it, which is, angle "a", is equal to a side labeled, "B", over the sine * opposite of that side, which is the angle "b".

In short, you end up with, $$\frac{Side\ A}{Angle\ a}=\frac{Side\ B}{Angle\ b}$$, and you can add the third side the same way: $$\frac{Side\ A}{Angle\ a}=\frac{Side\ B}{Angle\ b}=​​\frac{Side\ C}{Angle\ c}$$

$$\frac{sin(70)}{5.7}=\frac{x}{5} \\ \\ sin(x)*5.7=sin(70)*5 \\ \\sin(x)=\frac{5sin(70)}{5.7} \\ \\x=sin^{-1}(\frac{5sin(70)}{5.7})$$

I do hope the math is correct.

From here, you can just plug it in!

I hope you did take away something from my answer!

-TheLovely1

Jul 26, 2020
edited by TheLovely1  Jul 26, 2020