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Use the Law of Sines to find the values of x and y. Round to the nearest tenth.

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how do i use this to find Y i think i know how to get x
one second

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i have \[\frac{ \sin 22 }{ x }=\frac{ \sin 119 }{ 5 }\] \[5 (\sin 22)= x(\sin 119)\] \[\frac{ 5 (\sin 22) }{ \sin 119 }=\frac{ x (\sin 119) }{ \sin 119}\]
you can do that too
\[\frac{ 5 \sin 22 }{ \sin 119}=x\]
yep, pop that into the calc if you want. You can also use SOH CAH TOA, but the problem wants you to use the law of sines. You are correct, but get someone else to check
for ^^ i got 2.14153986217=x
ok so how do i get Y
The method is the same, you just need to know the measure of the angle that is opposite y. Since you know the measures of the other 2 angles, how could you find the measure of that third angle?.... :)
Right. so that gives you the angle opposite y. Now just set up your law of sines ratios using that angle and y, with 5 and sin(119*)
^^yes, good.... now find y. :)
\[\frac{ \sin 39 }{ y }=\frac{ \sin119 }{ 5 }\] \[5 \sin 39= Y \sin 119\] \[\frac{5 \sin 39 }{ \sin 119 }=\frac{ Y \sin 119 }{\sin 119 }\] \[\frac{ 5 \sin 39 }{ \sin 119 }=y\] y=3.59768014551
y approx. 3.6
And here is a Law of Sines tip I like to teach my students: You set up the first one as : \(\Large \frac{ \sin 22 }{ x }=\frac{ \sin 119 }{ 5 }\) which is COMPLETELY FINE and perfectly correct. :) BUT, you can also put the sides lengths in the num'r and the sine values in the den'r, that's equivalent: \(\Large \frac{x}{ \sin 22 }=\frac{5}{ \sin 119 }\) Now you're thinking, "so if it's the same thing, then why are you bothering to tell me this??" Well, the reason is that, if you compare the two, I think you'll agree that the 2nd version is algebraically easier to deal with, when you're solving for x. Just one step: multiply both sides by sin(22). So I find that preferable. And you can get away with it, since you will never have a 0 den'r, since the sine values won't be 0 as long as you truly have a triangle! (Could only get a sine=0 if you had an angle of 0 or 180). so the point is: put the UNKNOWN in the den'r, and it will simplify the process of solving for that unknown. :) If the angle is the unknown, put sines in num'r and sides in den'r; vice versa if the side is your unknown. :)
Yes, good job, that's what i got for y too. :)
Ah, poo.... typed all that out and made a mistake at the end, lol.... *put the UNKNOWN in the NUM'R!! not the den'r. lol
thanks :))
yw :)

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