Question

Law of sines, help!

Answer 1

solve for the missing side lengths

Answer 2

Oh they labeled the vertices A, B and C.
That's helpful.

Do you see which side they gave us?
Side length b=14, ya?

Answer 3

-Yes I see this

Answer 4

@zepdrix cant you set up the equation like so-given the info on the triangle already;
sin112/x=sin28/14

Answer 5

just so we're clear about which side you're calling x.

Answer 6

BTW, you can flip both sides of the fraction if it's more useful for you.\[\large\rm \frac{x}{\sin(112)}=\frac{14}{\sin(28)}\]

Answer 7

okay so at this point I am interested in finding x first, can we do that/ or is it smarter to find y?

Answer 8

okay let me try. I mean its the same as the last one. Just gotta use cross multiplication

Answer 9

Notice how the x is no longer in the denominator?
Makes things a little easier :)

Unless you're cross multiplying, then I guess it doesn't matter.

Answer 10

You don't NEED to cross multiply though.
Notice that x is being divided by sin(112),
so you only need to multiply both sides by sin(112) to isolate the x.

No big deal though

Answer 11

So then sin112(14)/sin28

Answer 12

oh okay!

Answer 13

oh youre saying if we flipped it. Okay

Answer 14

14sin(112)/sin(28)

ok looks good.
Calculator time :)

Answer 15

Yes, sorry.
If we had flipped it, then cross-multiply is not necessary.

Answer 16

okay but to me the cross multiply way seems more clear

Answer 17

Ok np :)

Answer 18

so lets just stick with it. Im going to plug it into a calculator

Answer 19

Well I get 27.65 but I want it as a number with a square root.

Answer 20

Oo I don't think we can leave it as an exact value for this problem...
112 and 28 are strange values, it would require a ton of work.
You want to approximate :) 27.65 sounds good!

Answer 21

really? Okay cool.

Answer 22

now we have to find the other side

Answer 23

cant we just say (sin28/14)/(sin40/y)

Answer 24

oops I meant to set those equal

Answer 25

Good good good.
Notice that you COULD use the other set of values,
but since your x is an `approximation`, it's better to use the side that is not x :)

Answer 26

sin28/14=sin40/y

Answer 27

ya, good times

Answer 28

Yes, cool

Answer 29

I get y=19.17

Answer 30

Mmm k good \c:/