Question

@robtobey @jhonyy9 @AkashdeepDeb

What is the value of B in this diagram?

A.12
B.10.2
C.9
D.8

Answer 1

i know its the law of Cosines

Answer 2

but im not sure how to substitute the values correctly
\[a ^{2}=b^2+c^2-2bc*\cos(A)\]

Answer 3

@ganeshie8

Answer 4

You need to use \[b^2=a^2 + c^2 -2ac * \cos(B)\]

Answer 5

Since you want to find b

Answer 6

okay then what do i sub for \[b^2\]

Answer 7

Nothing, b is the value you are looking for. Once you figure out what equals b^2, take the square root of it to find b.

Answer 8

Use the law of sines to find angle B

Answer 9

so \[b^2=12^2+6.33^2-2(12)(6.33)*\cos(113.17)\]

Answer 10

No, you have to find angle B using the law of sines. You put angle A where angle B should be. Do you know the law of sines?

Answer 11

\[sinA/a=sinB/b=sinC/c\]

Answer 12

Yes. First use it to find angle C:

\[12/(\sin113.17)=6.33/sinC\]
\[(6.33\sin113.17)/12=sinC\]
\[\sin^-1((6.33\sin113.17)/12)=C\]
C=29.01°

Answer 13

Now find angle B using angles A and C:

180-(29.01+113.17)
=37.82

Answer 14

Then plug that into your formula:

\[b^2=12^2+6.33^2-2(12)(6.33)\cos37.82\]

Answer 15

8. But why would I use sines? Cosines is to find any angle or the unknown side length....which is what i need to find, isn't it?

Answer 16

Yes, you're right. Both law of sines and law of cosines are used for finding any angle or unknown side length.

Answer 17

8 is the correct answer.

Answer 18

We use law of sines or law of cosines depending on what information we are given and what we need to find.

Answer 19

ooohhh okay :) i still dont understand it fully, and I have 4 more questions about sines and cosines application

Answer 20

I'm sorry, I'm not very good at explaining things :)

Answer 21

its alright. I am horrible in math, i mean HORRIBLE!!

Answer 22

if i tag you in a few other questions would you mind helping me?

Answer 23

You're not horrible. Math is all about applying the use of formulas and theorems. You just need to keep practicing, learn to use what you're given to deduce a way to find your answer. If you keep working at it, you'll get better. And we here at Open Study will always be around when you're stuck on something :)

Answer 24

I can't, I'm sorry :( I'm just leaving. But open a new question and try tagging ganeshie again and a few others. I'm sure someone can help :) Good luck!

Answer 25

Thank you!!