Question

Find the value of a .

Answer 1

I seriously just did a problem like this but I always forgot on how to use it

Answer 2

HI!!

Answer 3

looks like a law of cosines problem?

Answer 4

sine law again.

Answer 5

hmm i think you need cosines for this
you do not know any angle opposite one of the known sides

Answer 6

right you are. Cosine law required.

Answer 7

\[\frac{ \sin52 }{ ? } = \frac{ sinb }{ 4 }\]

Answer 8

\[a^2=b^2+c^2-2bc\cos(A)\]
\[a^2=4^2+7^2-2\times 4\times \cos(52^\circ)\] and a calcullator

Answer 9

hold the phone dear

Answer 10

if you want to use the law of sines (which you do , because it is easiest) you need 3 out of the for numbers to make a ratio

Answer 11

you do not have three out of any four, because you do not know the angle opposite any known side

Answer 12

you can see you ran in to that problem when you wrote
\[\frac{ \sin52 }{ ? } = \frac{ \sin(b) }{ 4 }\]

Answer 13

you got only two of the four numbers, two are unknown
so you must use the law of cosines for this one

Answer 14

@misty1212 i got 5.52507014 from doing your way after square rooting

Answer 15

i can check if you like, i didn't do it

Answer 16

@misty1212 i think it's right but can you check it please

Answer 17

http://www.wolframalpha.com/input/?i=sqrt%284%5E2%2B7%5E2-2*4*7*cos%2852%29%29

Answer 18

5.52 rounded looks good

Answer 19

@misty1212 could you help me with another problem? please

Answer 20

or in your case 5.5 cause they rounded to one decimal place

Answer 21

yeah but i can't read what they are trying to find the value of
in this case you know two angles so you know all three and therefore you can use the law of sines

Answer 22

what do they want, \(r\) ?

Answer 23

@misty1212 trying to find the value of r which is reallyw eird

Answer 24

ok what is the measure of the angle opposite \(r\)?

Answer 25

@misty1212 there's no angle opposite of r that's the weird part

Answer 26

of course there is lol

Answer 27

it is labelled \(\huge R\)

Answer 28

@misty1212 there isn't!!

Answer 29

oh i see, you mean you don't know what it is

Answer 30

lets find it
total in the triangle is 180 so it is
\[180-45-63=72\]

Answer 31

@misty1212 oooh yeah lmao forgot you could do it like that

Answer 32

now law of sines finishes it right?

Answer 33

\[\frac{r}{\sin(72)}=\frac{22}{\sin(45)}\] etc

Answer 34

@misty1212 so it's rearrange to 22sin72=rsin45?

Answer 35

this time i notice they round to two places
http://www.wolframalpha.com/input/?i=22sin%2872%29%2Fsin%2845%29

Answer 36

that step is not necessary

Answer 37

\[\frac{r}{\sin(72)}=\frac{22}{\sin(45)}\iff r=22\times\frac{ \sin(72)}{\sin(45)}\]

Answer 38

i know some math teacher might have said "cross multiply" but they are silly
\[\frac{x}{a}=\frac{b}{c}\iff x=\frac{ab}{c}\]

Answer 39

@misty1212 r=29.58993453?

Answer 40

yeah looks good

Answer 41

@misty1212 thank you!!! you really helped me tonight htis lesson really got me messed up

Answer 42

you're welcome!\[\huge \color\magenta\heartsuit\]