Question

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

Answer 1

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

Answer 2

i saw that to begin with

Answer 3

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

Answer 4

or does w mean the height?

Answer 5

i believe w is height

Answer 6

im not entirely sure

Answer 7

then sin42= w/102

Answer 8

and cos 42= (2/x)/102

Answer 9

cos42= (x/2)/102****

Answer 10

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

Answer 11

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

Answer 12

cos42= (x/2)/102

Answer 13

pythagoras

Answer 14

half of \(x\) is \(\sqrt{102^2-68^2}\)

Answer 15

can i have a fraction in the numerator

Answer 16

so \(x=2\sqrt{102^2-68^2}\)

Answer 17

http://www.wolframalpha.com/input/?i=2sqrt%28102^2-68^2%29

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

^^confused -_-

Answer 22

@ganeshie8 any help

Answer 23

\(\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"}\)

Answer 24

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

Answer 25

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

Answer 26

ive done confused myself again

Answer 27

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

Answer 28

aw heck imma use @satellite73 s method

Answer 29

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

Answer 30

but that doesnt look right

Answer 31

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

Answer 32

i dont understand now to use it with this problem

Answer 33

for x

Answer 34

okay wild katherine has appeared.