highschoolmom2010
Find the values of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.



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katherine.ok
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you have multiple ways. one is to recognize that this is isoceles triangle ( the triangle shape with two equal sides)

highschoolmom2010
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i saw that to begin with

katherine.ok
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which makes the right triangle have internal sum of 90+ 42+w= 180.

katherine.ok
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or does w mean the height?

highschoolmom2010
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i believe w is height

highschoolmom2010
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im not entirely sure

katherine.ok
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then sin42= w/102

katherine.ok
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and cos 42= (2/x)/102

katherine.ok
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cos42= (x/2)/102****

highschoolmom2010
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\[(102)*\sin 42=\frac{ w }{ 102 }*102\]
\[102 \sin 42=w\]
w\[\approx 68\]

highschoolmom2010
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so how now that i have found w how do i get x?

katherine.ok
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cos42= (x/2)/102

anonymous
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pythagoras

anonymous
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half of \(x\) is \(\sqrt{102^268^2}\)

highschoolmom2010
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can i have a fraction in the numerator

anonymous
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so \(x=2\sqrt{102^268^2}\)


jdoe0001
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@highschoolmom2010 you can always just use the cosine of 42 degrees you know
don't spare functions with your SOH CAH TOA

katherine.ok
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Satelite using wolfram alpha. LOL hes definitely not highschool student.

katherine.ok
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cos42=x/204= (x/2)/102 (the one i typed few mins ago)

highschoolmom2010
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^^confused _

highschoolmom2010
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@ganeshie8 any help

jdoe0001
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\(\bf sin(42^o) = \cfrac{\textit{opposite side}}{\textrm{hypotenuse}} \implies \cfrac{w}{102} \implies \color{blue}{sin(42^o) \times 102} = w\\
cos(42^o) = \cfrac{\textit{adjacent side}}{\textrm{hypotenuse}} \implies \cfrac{\textit{half of "x"}}{102} \implies \color{green}{cos(42^o) \times 102} = \textit{half of "x"}\)

highschoolmom2010
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\[\cos (42)\rightarrow 65*102\]

jdoe0001
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well, if "half of x" = 65, yes

highschoolmom2010
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ive done confused myself again

jdoe0001
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then again, if you already know that x= 65 * 2, you don't have to do the cosine part :)

highschoolmom2010
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aw heck imma use @satellite73 s method

highschoolmom2010
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\[\sqrt{108^2+68^2}=10868=40\]
\[\sqrt{40}=2\sqrt{10}\]

highschoolmom2010
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but that doesnt look right

jdoe0001
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using the cosine, I get ahemm, something else for "x"

highschoolmom2010
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i dont understand now to use it with this problem


katherine.ok
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okay wild katherine has appeared.

highschoolmom2010
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dw:1376262142492:dw

katherine.ok
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cos42=x/204

highschoolmom2010
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:( math is really hard for me right now yall

katherine.ok
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x=204*cos42.

highschoolmom2010
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ya know that makes it a whole lot easier

katherine.ok
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now the number should be above 150, which is so much more amazing than just sqrt(40).


highschoolmom2010
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ty @katherine.ok @satellite73 @jdoe0001