Question

Solve for x. Round your answer to 2 decimal places.

(picture below)

** medal & fan

Answer 1

do you know what the law of sines is?

Answer 2

um, i dont think i have covered that yet.

Answer 3

Does this look familiar to you at all?

\(\large\frac{a}{Sin A}=\large\frac{b}{Sin B}=\large\frac{c}{Sin C}\)

Answer 4

no, i definitely have not covered that yet :-(

Answer 5

fair enough. I'm not sure how I would solve a problem like this without that, sorry

Answer 6

recall you SOH CAH TOA \(\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}

\\ \quad \\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}\)


which identity uses the
angle
adjacent side, and
hypotenuse

only?

Answer 7

cosine

Answer 8

yeap

thus... one sec

Answer 9

i will wait for you :-)

Answer 10

\(\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\implies hypotenuse=\cfrac{adjacent}{cos(\theta)}\qquad thus
\\ \quad \\
cos(58^o)=\cfrac{17}{x}\implies x=\cfrac{17}{cos(48^o)}
\)

Answer 11

hmmm my 58 turned into a 48 for whatever reason =)
\(\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\implies hypotenuse=\cfrac{adjacent}{cos(\theta)}\qquad thus
\\ \quad \\
cos(58^o)=\cfrac{17}{x}\implies x=\cfrac{17}{cos(58^o)}\)

Answer 12

notice, you're using degrees, thus, make sure your calculator is in Degree mode when getting the cosine

Answer 13

x = 17 / 0.53 ?

Answer 14

yeap

Answer 15

i got it!! thank you so much!! that was really simple!!