highschoolmom2010 Group Title Use the Law of Sines to find the values of x and y. Round to the nearest tenth. 11 months ago 11 months ago

1. highschoolmom2010 Group Title

2. highschoolmom2010 Group Title

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

3. OffnenStudieren Group Title

one second

4. OffnenStudieren Group Title

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5. highschoolmom2010 Group Title

i have $\frac{ \sin 22 }{ x }=\frac{ \sin 119 }{ 5 }$ $5 (\sin 22)= x(\sin 119)$ $\frac{ 5 (\sin 22) }{ \sin 119 }=\frac{ x (\sin 119) }{ \sin 119}$

6. OffnenStudieren Group Title

you can do that too

7. highschoolmom2010 Group Title

$\frac{ 5 \sin 22 }{ \sin 119}=x$

8. OffnenStudieren Group Title

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

9. highschoolmom2010 Group Title

for ^^ i got 2.14153986217=x

10. highschoolmom2010 Group Title

ok so how do i get Y

11. DebbieG Group Title

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?.... :)

12. highschoolmom2010 Group Title

180-119-22

13. DebbieG Group Title

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*)

14. highschoolmom2010 Group Title

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15. DebbieG Group Title

^^yes, good.... now find y. :)

16. highschoolmom2010 Group Title

$\frac{ \sin 39 }{ y }=\frac{ \sin119 }{ 5 }$ $5 \sin 39= Y \sin 119$ $\frac{5 \sin 39 }{ \sin 119 }=\frac{ Y \sin 119 }{\sin 119 }$ $\frac{ 5 \sin 39 }{ \sin 119 }=y$ y=3.59768014551

17. highschoolmom2010 Group Title

y approx. 3.6

18. DebbieG Group Title

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. :)

19. DebbieG Group Title

Yes, good job, that's what i got for y too. :)

20. DebbieG Group Title

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

21. highschoolmom2010 Group Title

thanks :))

22. DebbieG Group Title

yw :)