Need help with precalculus will give owl bucks

- matlee

Need help with precalculus will give owl bucks

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- matlee

##### 1 Attachment

- matlee

For each triangle , determine the indicated value

- matlee

I know this is Cosine rule, but not sure how to start.

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## More answers

- Zale101

|dw:1450407256242:dw|

- Zale101

You are right, you need a cosine rule for this. Do you have an idea of what the rule says for cosine?

- matlee

To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule
is used when we are given either a) two angles and one side, or b) two sides and a non-included
angle. The cosine rule is used when we are given either a) three sides or b) two sides and the
included angle.

- matlee

##### 1 Attachment

- matlee

I think its that one

- Zale101

Cosine rule states:
\(a^2=b^2+c^2-2bc*cos(A)\)
\(b^2=a^2+c^2-2ac*cos(B)\)
\(c^2=a^2+b^2-2ab*cos(C)\)

- Zale101

Keep in mind, you are solving for only C. Which is the correct equation to use?

- matlee

O lol , c^2

- Zale101

Yes.

- matlee

wait thats what i put

- matlee

i got confused

- Zale101

You need to use this equation \(c^2=a^2+b^2-2ab*cos(C)\)

- matlee

ok

- Zale101

Now, plug the a, c, and b and solve for C. Can you do that?

- matlee

wait wait before we proceed can yo usee if i used the right rule for this one

- Zale101

You are right.

- matlee

I used thee sine rule

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- matlee

but cosine rule says if you have two sides and inlcuded angle then use cosine rule but i have included angle and i used sine rule

- Zale101

Yes. Because you got the degree and the side for A and a side for b. All you have to do is:
\(\Large\frac{sin(A)}{a}=\frac{sin(B)}{b}\)
\(\Large\frac{sin(70Â°)}{7}=\frac{sin(B)}{4}\)
Cross multiply and solve for B, don't forget to use inverse sine to solve for B at the end.

- Zale101

Same thing for cosine rule equation you had, don't forget to use inverse cosine to solve for C.

- matlee

o man im so confused i had asked a question earlier and he did it without the inverse cosine

- Zale101

Ok. I have a good idea. How about you show your work here or write it on paper and take a picture of it.

- Zale101

You take the inverse to both sides in order to solve for C.

- matlee

Ok thank you i will do it right now. OOO. This one i had to solve for side a

- matlee

the one that he did not do inveerse

- Zale101

\(c^2=a^2+b^2-2ab*cos(C)\)
Plug these in: a=6, b=12, c=17
\(17^2=6^2+12^2-2(6)(12)*cos(C)\)
\(289=180-144*cos(C)\)

- Zale101

Is that what you had?

- matlee

haha no i am writing them right now but yes.

- Zale101

I have a question for you.

- matlee

Ok

- Zale101

When you knew that you had to use the cosine rule, did you plug in a,b, and c or you did not attempt this question at all?

- matlee

No i did not attempt the question at all because i couldnt tell if i did it right, also i just learned this three open study questions ago

- Zale101

Okay, can you show your work here by typing it out?

- matlee

##### 1 Attachment

- matlee

im stuck

- Zale101

\(\Large-\frac{109}{144}=cos(C)\)

- Zale101

What happens if you take the inverse cos to both sides? Have you learned about this before?

- matlee

Yes but i barely pay attention in class.

- matlee

wait how did u get 109/144

- matlee

someone taught me about inverse last open study question

- matlee

oh i see because u subrtracted 180 from 289 and since -144 is connected to cos you have to divide

- matlee

do i have to use inverse now?

- Zale101

\(289=180-144*cos(C)\)
subtract 180 to both sides
\(289-180=180-180-144*cos(C)\)
\(109=-144*cos(C)\)
divide -144 to both sides
\(109=-144*cos(C)\)
\(\Large \frac{109}{-144}=\frac{-144*cos(C)}{-144}\)
\(\Large-\frac{109}{144}=cos(C)\)

- Zale101

Yes, use the inverse now.
Here's an example of how an inverse operates.
|dw:1450408919922:dw|

- Zale101

\(\Large cos^{-1}(cos(x))=x\)
the cosines will reverse and cancel out which will equal x

- Zale101

Do the same when solving for C.

- matlee

Ok. Wait what is X?

- matlee

nvm i got it lol

- matlee

2.42942=x

- Zale101

Yes..
:)

- Zale101

That's your C.

- matlee

yay is that C?

- Zale101

X and y are just examples.

- matlee

Thank you!

- Zale101

No problem! :)

- matlee

Can you vrvbhelp me iwth more!Its not value anymore its are aof triangle

- matlee

@Zale101 i want to give you owl bucks but i have 9 and it says i dont have enough to send but i have sent less than 9 before when i had 10 owl bucks.

- Zale101

That's okay. I don't need no owlbucks.

- matlee

lol ik now

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