Question

Law of sines question!

Answer 1

What is the value of x?

Answer 2

Remember your law of sines? :)
\(\large\rm \frac{\sin(A)}{a}=\frac{\sin(B)}{b}\)

Where side a is opposite angle A, and same for the b's.

Answer 3

So um...
which angle is opposite the side length labeled 14? :)

Answer 4

yes, which one is angle a,b, and c in this case though?

Answer 5

14 and 45 match and x and 60 match

Answer 6

Good good good :)
So thats the information we'll want to use.

Answer 7

is 14 A?

Answer 8

I was calling the angles the capital letters,
so I guess A=45, a=14, ya? ^^

Answer 9

yes, makes sense

Answer 10

Do you think you can plug in the pieces of information correctly?
Get this kind of setup? :)\[\large\rm \frac{\sin(A)}{a}=\frac{\sin(B)}{b}\]

Answer 11

14/45=x/60

Answer 12

Oh boy, you didn't use your sine function at all XD

Answer 13

sin14/sin45=sinx/sin60

Answer 14

Oh you :P lol

Answer 15

the sine dosnt go before the denominator does it?

Answer 16

Correct, we apply sine to `angles`.

Answer 17

numerator*

Answer 18

The denominator is a side length :)
No sine for him.

Answer 19

okay

Answer 20

wait so then shouldnt it be 45sin/15 and 60sin/x

Answer 21

Mmm ok looks good besides that small typo you made :)\[\large\rm \frac{\sin(45)}{14}=\frac{\sin(60)}{x}\]Now we solve for x.
Just a few little algebra tricks.

Answer 22

oh I misrea what you wrote lol XD

Answer 23

darn I spilled the beans :d

Answer 24

When we take this proportion,
the `sine of an angle` to the `side opposite that angle`,
Law of Sines is telling us that this proportion is always the same regardless of which side/angle pair we choose.

Answer 25

yes

Answer 26

Anyway, we take the sine of the angles,
the angles are 45 and 60 degrees in this case.
sin(45)/14 = sin(60)/x

Hopefully that's not too confusing D:

Answer 27

so what we already did was right

Answer 28

Yes, we're here currently :)\[\large\rm \frac{\sin(45)}{14}=\frac{\sin(60)}{x}\]Have you learned about your "special angles" yet?
sin(45) and sin(60) work out to nice values that we don't need a calculator for.

Answer 29

Hmm I may have but i need a refresher