I need help on this, please?
The vertices of a triangle are A(7, 5), B(4, 2), and C(9, 2). What is m?
A. 30°
B. 45°
C. 56.31°
D. 78.69°

- anonymous

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- misty1212

HI!!

- anonymous

hey

- misty1212

that is a good question, what is \(m\)? not clear at all since none of the vertices are labelled "m"

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## More answers

- anonymous

- misty1212

here is a nice picture of your triangle
i don't see any m in it though
http://www.wolframalpha.com/input/?i=triangle+%287%2C+5%29%2C+%284%2C+2%29%2C+%289%2C+2%29

- anonymous

yeah, that doesn't help me.. I don't even understand what the question is tell me nor Geometry it self?

- misty1212

look carefully at your question
you are given the vertices of a triangle, with points labelled A, B, C
but then you ask for an angle m
there is no m in sight, only A, B, C

- anonymous

but thats all it gives me?? hmm?

- misty1212

m usually stands for the measure of some angle
but that would be "find m

- jim_thompson5910

\[\Large m\angle ABC\] means "angle ABC" where B is the vertex of the angle
something like this
|dw:1436923873975:dw|

- anonymous

Here's the question, maybe this is better?

##### 1 Attachment

- jim_thompson5910

First you use the distance formula to find the distance from A to B. That will give you the length of AB. Do the same for BC and AC

- jim_thompson5910

tell me what distances you get

- anonymous

Alrighty ^-^

- anonymous

My work ^-^

##### 1 Attachment

- jim_thompson5910

I don't agree with your last distance of 13

- jim_thompson5910

you forgot to take the square root of 13

- anonymous

oh

- anonymous

Square root of 13 is 3.60

- jim_thompson5910

|dw:1436929152566:dw|

- jim_thompson5910

|dw:1436929181793:dw|

- jim_thompson5910

a = 5
b = 3.60555
c = 4.24264
use these three values in the law of cosines formula
b^2 = a^2 + c^2 - 2*a*c*cos(B)
to solve for the value of B

- anonymous

-173.8115277? Thats what I got?

- jim_thompson5910

b^2 = a^2 + c^2 - 2*a*c*cos(B)
3.60555^2 = 5^2 + 4.24264^2 - 2*5*4.24264*cos(B)
are you able to isolate cos(B) ? If not, try replacing "cos(B)" with "x"
ie, solve for x in
3.60555^2 = 5^2 + 4.24264^2 - 2*5*4.24264*x

- anonymous

For 5^2+4.24264^2-2*5*4.24264*x=42.99999417
then 3.60555^2 =12.9999908
and then I'm stuck, If I'm getting any of this right??

- jim_thompson5910

`5^2+4.24264^2-2*5*4.24264*x` will turn into `42.9999941696 - 42.4264*x`

- jim_thompson5910

42.9999941696 - 42.4264*x = 12.9999908025
-42.4264*x = 12.9999908025 - 42.9999941696
-42.4264*x = -30.0000033671
x = -30.0000033671/(-42.4264)
x = ???

- anonymous

Dont understand

- jim_thompson5910

where are you stuck at?

- anonymous

all of this.. I get .7071069751?

- jim_thompson5910

yes x = 0.7071069751

- anonymous

oh so I was doing all that right?

- jim_thompson5910

you agree that
5^2 = 25
3.60555^2 = 12.9999908025
4.24264^2 = 17.9999941696
2*5*4.24264 = 42.4264
right?

- jim_thompson5910

yeah if you got to x = 0.7071069751, then you are doing it right

- anonymous

yeah and awesome

- jim_thompson5910

recall that I replaced "cos(B)" with "x" to make things simpler

- jim_thompson5910

if x = 0.7071069751
then cos(B) = 0.7071069751

- anonymous

oooh theres more work???

- jim_thompson5910

to find B itself, we apply the arccosine function to both sides
cos(B) = 0.7071069751
arccos(cos(B)) = arccos(0.7071069751)
B = ???

- jim_thompson5910

just these last steps and you're done

- anonymous

your killing me man, your killing me haha

- jim_thompson5910

lol
what is `arccos(0.7071069751)` equal to ?

- jim_thompson5910

use a calculator like this one if you don't have a calculator with arccos
http://web2.0calc.com/

- anonymous

I got .7602444711?

- jim_thompson5910

http://web2.0calc.com/#arccos(0.7071069751)

- jim_thompson5910

once you click the link, hit enter to have it evaluate

- anonymous

round it up its 45. Cool

- jim_thompson5910

yeah 44.999984287488 ---> 45

- anonymous

awesome, Its correct. Thank you, alot

- jim_thompson5910

you're welcome

- anonymous

Means a lot ^-^

- jim_thompson5910

I'm glad to be of help

- anonymous

Yay! lol

- ali2x2

Close the question, But not before you give me a medal :3

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