Question

Find the measure of angle X in the triangle below.
I'm supposed to use the law of sines, but I'm not sure how to solve it.

Answer 1

\(\normalsize\color{red}\bigstar\large\color{gold}\bigstar\Large\color{greenyellow}\bigstar\large\color{cyan}\bigstar\normalsize\color{blue}\bigstar\large\color{purple}\bigstar\Large\color{magenta}\bigstar\large\color{pink}\bigstar\normalsize\color{orchid}\bigstar\large\color{red}\bigstar\Large\color{gold}\bigstar\large\color{greenyellow}\bigstar\Large\color{cyan}\bigstar\large\color{blue}\bigstar\normalsize\color{purple}\bigstar\large\color{magenta}\bigstar\Large\color{pink}\bigstar\large\color{orchid}\bigstar\normalsize\color{red}\bigstar\\\Large\frak\rlap{\huge\color{red}{W}\Large\color{gold}{E}\color{greenyellow}{L}\color{lime}{C}\color{cyan}{O}\color{blue}{M}\color{purple}{E}~\color{orchid}{T}\color{pink}{O}~\huge\color{red}{O}\Large\color{gold}{P}\color{greenyellow}{E}\color{lime}{N}\huge\color{cyan}{S}\Large\color{blue}{T}\color{purple}{U}\color{magenta}{D}\color{orchid}{Y}\color{pink}{!}}{\huge\color{black}{\; W}\Large\color{black}{ELCOME~TO}\huge\color{black}{O}\Large\color{black}{PEN}\huge\color{black}{S}\Large\color{black}{TUDY!}}\\\hspace{43 pt}\Large\bf\color{gold}♔\hspace{60 pt}\huge\color{gold}☀\\\hspace{24 pt}\huge\bf\color{orangered}૮\hspace{-3 pt}\Large\color{gold}{(}\color{greenyellow}◕\hspace{1 pt}\color{lime}ᴥ\hspace{1 pt}\color{cyan}◕\color{blue}{)}\hspace{-2 pt}\LARGE\color{purple}ა\\\hspace{14 pt}\large\color{orangered}☁\color{orange}☁\hspace{-7 pt}\Large\bf\color{red}{◝}\color{red}{(}\hspace{-2 pt}\large\color{orangered}つ\hspace{13 pt}\Large\color{lime}{)}\hspace{-3 pt}\large\color{cyan}つ\small\color{magenta}━\color{magenta}━\small\color{orchid}◇\normalsize\color{pink}☆\large\color{red}\bigstar\small\color{gold}☆\small\color{yellow}◇\small\color{lime}\bigstar\Large\color{greenyellow}☆\normalsize\color{cyan}\bigstar\small\color{blue}☆\color{purple}◇\color{magenta}\bigstar\scriptsize\color{orchid}☆\color{pink}◇\\\hspace{4 pt}\Large\cal\color{red}☁\color{orangered}☁\Large\cal\color{orange}☁\rlap{\hspace{2 pt}\Large\cal\color{gold}{☁}\hspace{1 pt}\color{greenyellow}{☁}\color{cyan}{☁}\color{blue}☁\color{purple}☁\color{magenta}☁\color{orchid}☁\color{pink}☁\color{red}☁\color{orangered}☁\color{orange}☁\color{gold}☁\color{greenyellow}☁}{\hspace{1 pt}\normalsize\bf\color{orangered}{⁀}\hspace{3 pt}\color{greenyellow}{⁀}}\\\LARGE\cal\color{red}☁\color{orangered}☁\color{gold}☁\color{greenyellow}☁\color{cyan}☁\color{blue}☁\color{purple}☁\color{magenta}☁\color{orchid}☁\color{pink}☁\color{red}☁\color{orange}☁\color{gold}☁\color{greenyellow}☁\\\normalsize\color{red}\bigstar\large\color{gold}\bigstar\Large\color{greenyellow}\bigstar\large\color{cyan}\bigstar\normalsize\color{blue}\bigstar\large\color{purple}\bigstar\Large\color{magenta}\bigstar\large\color{pink}\bigstar\normalsize\color{orchid}\bigstar\large\color{red}\bigstar\Large\color{gold}\bigstar\large\color{greenyellow}\bigstar\Large\color{cyan}\bigstar\large\color{blue}\bigstar\normalsize\color{purple}\bigstar\large\color{magenta}\bigstar\Large\color{pink}\bigstar\large\color{orchid}\bigstar\normalsize\color{red}\bigstar\)

Answer 2

\({\huge\color{black}{\bigstar}\color{black}{\hspace{2pt}\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{lblack}{\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}~\color{black}{\hspace{4pt}\bigstar}\color{black}{\bigstar}~\color{black}{\hspace{6pt}\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{black}{\hspace{1.5pt}\bigstar}\color{black}{\hspace{1.5pt}\bigstar}}{\hspace-318pt\huge\color{red}{\bigstar}\color{orange}{\hspace{2pt}\bigstar}\color{goldenrod}{\bigstar}\color{yellow}{\bigstar}\color{lightgreen}{\bigstar}\color{green}{\bigstar}\color{turquoise}{\bigstar}~\color{royalblue}{\hspace{4pt}\bigstar}\color{purple}{\bigstar}~\color{#00bfff}{\hspace{6pt}\bigstar}\color{#00bfff}{\bigstar}\color{#00bfff}{\bigstar}\color{#11c520}{\bigstar}\color{#11c520}{\hspace{1.5pt}\bigstar}\color{#11c520}{\hspace{1.5pt}\bigstar}}\\\huge\bf\color{black}W\color{black}E\color{black}{\hspace5ptL}\color{black}{\;C}\color{black}{\;O}\color{black}M\color{black}{\,E~\;}\color{black}{\hspace{4.2pt}T}\color{black}{\:O}~~\color{black}{\hspace{4pt}Open}\color{black}{Study}\hspace-318pt{\huge\bf\color{red}W\color{orange}E\color{goldenrod}{\hspace5ptL}\color{yellow}{\;C}\color{lightgreen}{\;O}\color{darkgreen}M\color{turquoise}{\,E~\;}\color{royalblue}{\hspace{4.2pt}T}\color{purple}{\:O}~~\color{#00bfff}{\hspace{4pt}Open}\color{#11c520}{Study}}\\\huge\color{black}{\bigstar}\color{black}{\hspace{2pt}\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}~\color{black}{\hspace{5pt}\bigstar}\color{black}{\bigstar}~\color{black}{\hspace{6pt}\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{black}{\bigstar}\color{black}{\hspace1.5pt\bigstar}\color{black}{\hspace{1.5pt}\bigstar\hspace-318pt{\huge\color{red}{\bigstar}\color{orange}{\hspace{2pt}\bigstar}\color{goldenrod}{\bigstar}\color{yellow}{\bigstar}\color{lightgreen}{\bigstar}\color{green}{\bigstar}\color{turquoise}{\bigstar}~\color{royalblue}{\hspace{5pt}\bigstar}\color{purple}{\bigstar}~\color{#00bfff}{\hspace{6pt}\bigstar}\color{#00bfff}{\bigstar}\color{#00bfff}{\bigstar}\color{#11c520}{\bigstar}\color{#11c520}{\hspace1.5pt\bigstar}\color{#11c520}{\hspace{1.5pt}\bigstar}}}\\\large\bf {I~will~tag~some~users~that~may~be~able~to~help~you}\\\small\cal Made~by~@sleepyjess\)

Answer 3

Thank you!

Answer 4

@SithsAndGiggles @sleepyjess @amistre64 @iGreen @TheSmartOne @Xx_H20_Avenger_xX @undeadknight26

Answer 5

you're welcome!! :)

Answer 6

Law of Sines is fun! Do you know what the law of sines is?

Answer 7

yes, it's sinA/a=sinB/b=sinC/c
I solved it using this formula but came up with the answer 1, but I'm 99% thats not the right answer.

Answer 8

Okay, give me a minute or 2 to solve it myself, and we'll see if we got the same answer :)

Answer 9

ok :)

Answer 10

Okay, are you coming up with X \(\approx\) 1 or sin(X) \(\approx\) 1

Answer 11

I believe I'm coming up with X\[\approx \]1

Answer 12

Okay, can you show me your steps to get to that?

Answer 13

Sin67.38/24=X/26 then I cross multiply to get
X=26 sin67.38=24
X= 24/26 sin 67.38 after entering it into my calculator i get
X=1

Answer 14

That's where you made the mistake. You shouldn't cross multiply, just multiply by 26 to leave sin(X) on the right side

Answer 15

\(\dfrac{sin(67.38)}{24} = \dfrac{sin(X)}{26}\)

Multiply both sides by 26

\(\dfrac{26sin(67.83)}{24} = sin(X)\)

Answer 16

So would I find the sine of 67.83?

Answer 17

Yep, sin(67.83)*26 first

Answer 18

I multiplied the sine with 26 and got 24.07

Answer 19

That's about right, I got 23.99997643, depending on the calculator

Answer 20

now do that answer over 24

Answer 21

so 24.07/24?

Answer 22

Yep

Answer 23

so is that my answer?

Answer 24

Nope, that is the sin of X

Answer 25

What is the opposite of sin?

Answer 26

cosine

Answer 27

arcsin

Answer 28

some calculators have it as \(sin^{-1}\)

Answer 29

ok,i found it. So it would be sin-1 24.07/24?

Answer 30

Divide 24.07/24 before doing the arcsin though :)

Answer 31

Ok. I got 1

Answer 32

Should be slightly over 1, but then do the arcsin of that

Answer 33

My calculator gave me an error message.

Answer 34

wait, you can't do sin/arcsin of anything over 1

Answer 35

Okay, let's just go with 26*sin(67.38) = 23.99997643 /24 = .9999990179

Answer 36

so you don't have to type that out, arcsin of .999990179 \(\approx\) 89.92

Answer 37

Did you round anything in the first couple steps?

Answer 38

Ok, thank you so so much!

Answer 39

no, i didn't round anything until the end.

Answer 40

No problem :) Sorry, couldn't load anything

Answer 41

No worries :). Thank you for the help.