In △JKL, solve for x.
Answer Choices:
A) 66.73
B) 74.89
C) 15.44
D) 38.16

- anonymous

In △JKL, solve for x.
Answer Choices:
A) 66.73
B) 74.89
C) 15.44
D) 38.16

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- anonymous

##### 1 Attachment

- Nnesha

\[\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }\]

- Nnesha

|dw:1440790508463:dw|

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## More answers

- Nnesha

which function you should use to find x ?

- anonymous

The Cos function?

- Nnesha

which side is adjacent of 27 degree angle ?

- anonymous

Side KL with the 34 in the middle

- Nnesha

hmm that would be the opposite side
adjacent side would the touch |dw:1440790695818:dw| the angle
now look at 27 degree angle

- Nnesha

kl is adjacent of theta
it's a opposite side of 27 degree angle not adj

- anonymous

Oh, yes. I forgot about the Theta,

- Nnesha

to find length of x
you should know one angle and one side
so we would use sin function

- Nnesha

|dw:1440790850611:dw|

- anonymous

Wait, how'd you get the Adjacent onto the opposite side? Is it being flipped because of the 27 degrees?

- Nnesha

different angles different sides

- anonymous

|dw:1440791024957:dw|

- Nnesha

JK is n't opposite side of 27 angle

- Nnesha

yep right solve for x

- anonymous

Okay, just a second :)

- anonymous

|dw:1440791173523:dw|

- anonymous

Then my answer was: 74.906

- Nnesha

looks good

- anonymous

Are you sure everything looks right?

- Nnesha

i know what u r talking about
when you put sin(27 degree) into the calculator
you will get .45399
so you should round it
.45399=.4540

- Nnesha

|dw:1440791354591:dw|

- Nnesha

now divide 34/.4540

- anonymous

Yes, my answer is: 74.889, which will then round to 74.89. Which is B. :)

- Nnesha

yes :=)

- anonymous

Could you possibly help me on another question?

- Nnesha

i'll try

- anonymous

Okay, would you like it in a different post or here is fine?

- Nnesha

doesn't matter :=) post that here i'm okay with it

- anonymous

Find the value of the cot 10° using your calculator.
Answer choices:
A) 0.176
B) 5.671
C) 0.648
D) 1.542

- Nnesha

okay use calculator then :D

- anonymous

How would I type that in though?

- Nnesha

what is the reciprocal of cot ?

- anonymous

Hmm, I'm sorry haha, I don't understand this question at all, it wasn't in the lesson I got my notes from..

- Nnesha

alright then write these down in ur notebook \[\large\rm sin \theta = \frac{ 1 }{ \csc \theta }~~~\cos \theta=\frac{ 1 }{ \sec \theta}~~~\tan \theta=\frac{ 1 }{ \cot \theta }=\frac{ \sin \theta}{ \cos \theta}\]

- Nnesha

tan =1/cot or you can say it's equal to sin/cos

- Nnesha

csc , sec and tan are reciprocal of sin ,cos and cot

- Nnesha

csc = 1/sin
sin =1/csc

- Nnesha

so if tan = sin /cos
cot = ?

- anonymous

1?

- Nnesha

what is the reciprocal of sin/cos ?

- anonymous

tan.

- Nnesha

okay so cot =1/tan
\[\huge\rm tan = \frac{ 1 }{ \cot }~~and~~ \cot =\frac{ 1 }{ \tan}\]

- Nnesha

if tan equal sin/cos then
replace tan with sin /cos

- Nnesha

okay so cot =1/tan
\[\huge\rm \cot =\frac{ 1 }{ \color{red}{\tan}}\]\[\cot = \frac{ 1 }{ \color{Red}{\frac{ \sin }{ \cos }} }\]

- anonymous

Okay, so you're basically switching them around? With the originally formula.

- Nnesha

just remember tan =sin/cos

- Nnesha

yes right

- Nnesha

now cot = ??

- Nnesha

\[\huge\rm \frac{ 1 }{ \frac{ \sin }{ \cos } } = ?\]we can change division to multiplication right

- anonymous

I'm so confused, I'm understanding pieces but then I'm not.. As I said before, I've never seen this type of question or even demonstration in a lesson I've had.

- Nnesha

okay let's change that to simple algebra \[\huge\rm \frac{ 1 }{ \frac{ a }{ b } }\] how would you simplify it ?

- anonymous

Multiplying?

- Nnesha

multiply the `numerator` by the `reciprocal` of the bottom fraction \[\huge\rm \frac{ 1 }{ \frac{ a }{ b } }=1 \times \frac{b}{a}\]

- anonymous

Why did you change b as the numerator and a as the denominator?

- Nnesha

ohh so you don't know the definition of reciprocal
reciprocal means `flip` the fraction
reciprocal of 2/3 is 3/2

- Nnesha

so reciprocal of a/b would be b/a
so to change division to multiplication
you should always multiply the numerator with the `reciprocal` of the bottom

- anonymous

Oh okay, I understand.

- Nnesha

so what is reciprocal of sin/cos ?

- anonymous

Well, you said reciprocal means to flip the fraction, so would it be cos/sin? Or would it be csc/sec?

- Nnesha

no just cos /sin

- Nnesha

tan = sin/cos
and cot is `reciprocal` of tan then cot would be cos/sin

- Nnesha

\[\huge\rm cot \theta= \frac{ \cot \theta }{ \sin \theta }\]\[\huge\rm cot(10^o)= \frac{ \cos (10)^o }{ \sin(10^o) }\]

- anonymous

Okay, I understand what's going on now. So you'd fill in the 10 degrees with the cot function?

- Nnesha

another example \[\huge\rm \cot (a) =\frac{ \cos(a) }{ \sin(a)}\]

- Nnesha

yes you have to find cot (10 deg)
which is not in the calcualtor
so you should put cos(10)/sin(10)

- Nnesha

cot(10) is same as cos(10)/(sin 10)

- anonymous

It'll give me 5.671. Which is B. I'll have to review those functions more because it's still confusing but I can understand what you're saying. I'll just need to do some more practice.

- Nnesha

yes practice ,practice and practice you will become trig expert!

- Nnesha

let me know if you din't understand anything on this post i'll try my best to explain! :=)
good luck!

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