Question

Find x. Round to the nearest degree.

Answer 1

Know your trig ratios?

Answer 2

like the 30 60 90 rule and all that?

Answer 3

use the law of sines

http://www.mathsisfun.com/algebra/trig-sine-law.html

Answer 4

ok!

Answer 5

is that supposed to be a right triangle?

Answer 6

^ That's what I thought haha

Answer 7

sorta ambiguous =)

Answer 8

39/sin(x) ?

Answer 9

and that's equal to what?

Answer 10

and idk if it is a right trianlge this is all the information i was given

Answer 11

um b/sinb?

Answer 12

39/sin(x) is on the right track, but it's only half of what you need

Answer 13

oh I'm not thinking, the law of sines won't work here

Answer 14

but the law of cosines will

Answer 15

oh ok!

Answer 16

law of cosines

b^2 = a^2 + c^2 - 2ac*cos(B)

39^2 = 59^2 + 36^2 - 2*59*36*cos(x)

solve for x

Answer 17

ok im at 1521=529cos(x) is this correct so far

Answer 18

the left is right, but the right side is not

Answer 19

strange as that sounds...

Answer 20

you cannot go from 59^2 + 36^2 - 2*59*36*cos(x) to 529*cos(x)

Answer 21

oh whoops so how do you multiple and subtract all that

Answer 22

if it helps, think of cos(x) as a variable, say z

so 59^2 + 36^2 - 2*59*36*cos(x) is really 59^2 + 36^2 - 2*59*36*z

Answer 23

3481+1296-4248z
4777-4248z
529z
i keep getting this?

Answer 24

the jump from

4777-4248z

to

529z

is not a valid move

Answer 25

4777 and -4248z are NOT like or common terms. You cannot combine them

Answer 26

ooh!! so i have to multiple it by z first

Answer 27

the goal now is to solve for z (which essentially isolates cos(x))

Answer 28

when i did 4248cos in my calculator it came out as .3090 and like so on

Answer 29

Here's what you should have


39^2 = 59^2 + 36^2 - 2*59*36*cos(x)

39^2 = 59^2 + 36^2 - 2*59*36*z

1521 = 3481+1296-4248*z

1521 = 4777 - 4248*z

1521 - 4777 = -4248*z

-3256 = -4248*z

-4248*z = -3256

z = -3256/(-4248)

z = 0.766478

cos(x) = 0.766478

x = ???

Answer 30

oh you had to get it alone do i have to now move x over? or do i put it in my calculator like that?

Answer 31

what function undoes cosine?

Answer 32

divison?

Answer 33

no it's inverse cosine, aka arccosine

Answer 34

you apply the arccosine to both sides to isolate x

Answer 35

oh i never learned about that what is it

Answer 36

ok have a look at this page

http://www.themathpage.com/atrig/inverseTrig.htm

and tell me what you think

Answer 37

so you would like "switch" the x and .76647

Answer 38

no

Answer 39

we know that cos(60) = 1/2 correct?

Answer 40

i guess

Answer 41

so let's say we had

cos(x) = 1/2

and we had no idea that x was 60

Answer 42

we would apply the arccosine function to both sides to get

cos(x) = 1/2

arccos(cos(x)) = arccos(1/2)

x = 60

Answer 43

what kind of calculator do you have?

Answer 44

whatever one is on the iphone

Answer 45

does that have inverse trig functions on it?

Answer 46

no i dont think so

Answer 47

ok I recommend you use an online calculator

wolfram alpha and google are two good calculators

Answer 48

if you were to type

"arccos(0.766478) in degrees"

without quotes into google, you'd get your answer (make sure to round of course)

Answer 49

sorry I meant to say "arccosine(0.766478) in degrees"

enter that without quotes

Answer 50

so it would rounf to 40?

Answer 51

correct

Answer 52

It was thank you so much for your time!