a few law of sines questions! PLEASE HELP!!!

- cutiecomittee123

a few law of sines questions! PLEASE HELP!!!

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- Pinkpiggy

ok, shoot

- Pinkpiggy

ill try my best

- cutiecomittee123

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## More answers

- Pinkpiggy

What grade?

- cutiecomittee123

precalculus

- Pinkpiggy

ok, whats the question

- cutiecomittee123

find the missing sides and angles of that triangle using law of sines

- Pinkpiggy

ok, give me a min

- anonymous

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- cutiecomittee123

are you sure? the unit right now is just law of sines, but we can try law of cosines

- anonymous

the other angle you find easily because the sum is 180

- anonymous

what is the remaining angle?

- cutiecomittee123

Yeah so 180-45-15=120

- anonymous

you do not need the law of cosines, you have all three angles

- anonymous

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- cutiecomittee123

I think I have it from here, Idk why I was confused. Let me try this and Ill tell you guys what I get

- anonymous

\[\frac{a}{\sin(A)}=\frac{b}{\sin(B)}\] you know three of those four numbers

- cutiecomittee123

so 200/sinA=x/sin45

- anonymous

Angle B = 180-60 = 120 degrees
a =

- anonymous

no your equation is not right
use the one i wrote, but put in the numbers that you know

- cutiecomittee123

alright, I am officially stuck

- anonymous

do you see the equation i wrote above?

- cutiecomittee123

I knew the equation you gave me, I dont know which numbers to plug into it

- cutiecomittee123

which one is A, and which one is A

- anonymous

\[\frac{a}{\sin(A)}=\frac{b}{\sin(B)}\] look at the labelling of the triangle
what is angle A

- cutiecomittee123

B

- cutiecomittee123

x/45=200/sinB

- anonymous

it depends on how you label it, but you drew the picture with the angles labelled

- cutiecomittee123

oops I mean x/sin45=3200/sinB

- anonymous

wait hold on a second
i think i see what the problem is

- cutiecomittee123

ohh lol I forgot about the angle

- cutiecomittee123

x/sin45=200/sin120

- anonymous

in order to keep all of this striaight, we usually adopt the following convention
the side opposite angle \(A\) is \(a\) , the side opposite angle \(B\) is \(b\) and opposite \(C\) is \(c\)

- anonymous

that way \[\frac{a}{\sin(A)}=\frac{b}{\sin(B)}\] makes sense

- cutiecomittee123

Yeah so the equation I just posted should be right

- anonymous

no x's in other words

- anonymous

what side are you solving for?

- cutiecomittee123

so then a/sin45=200/sin120

- anonymous

bingo

- anonymous

making \[a=\frac{200\sin(45)}{\sin(120)}\] and a calculator

- cutiecomittee123

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- cutiecomittee123

When plugged into my calculator 200sin45/sin120=163.299
dont I take the inverse sin now?

- mathmate

@cutiecomittee123
To make things easier, we usually label angles of a triangle with a capital letter, and the OPPOSITE side with the lower case letter of the angle. See @satellite73 's figure, and there will be no confusion.

- anonymous

you are not looking for an angle you are looking for a side
whatever number you get is the answer

- anonymous

in other words, no, don't take the inverse sine

- anonymous

not that you could anyway, since there is no arcsine of a number larger than 1!

- cutiecomittee123

No, we are solving for the side I thought?

- anonymous

right, the side
so you are done

- cutiecomittee123

sweet, thanks for everyones help!!

- anonymous

yw

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