Question

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°

Answer 1

HI!!

Answer 2

hey

Answer 3

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

Answer 4

<ABC?* this was missing in the whole question, sorry

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

but thats all it gives me?? hmm?

Answer 9

m usually stands for the measure of some angle
but that would be "find m<A:for example

Answer 10

\[\Large m\angle ABC\] means "angle ABC" where B is the vertex of the angle

something like this

Answer 11

Here's the question, maybe this is better?

Answer 12

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

Answer 13

tell me what distances you get

Answer 14

Alrighty ^-^

Answer 15

My work ^-^

Answer 16

I don't agree with your last distance of 13

Answer 17

you forgot to take the square root of 13

Answer 18

oh

Answer 19

Square root of 13 is 3.60

Answer 20

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

Answer 21

-173.8115277? Thats what I got?

Answer 22

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

Answer 23

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??

Answer 24

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

Answer 25

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 = ???

Answer 26

Dont understand

Answer 27

where are you stuck at?

Answer 28

all of this.. I get .7071069751?

Answer 29

yes x = 0.7071069751

Answer 30

oh so I was doing all that right?

Answer 31

you agree that

5^2 = 25
3.60555^2 = 12.9999908025
4.24264^2 = 17.9999941696
2*5*4.24264 = 42.4264

right?

Answer 32

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

Answer 33

yeah and awesome

Answer 34

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

Answer 35

if x = 0.7071069751

then cos(B) = 0.7071069751

Answer 36

oooh theres more work???

Answer 37

to find B itself, we apply the arccosine function to both sides

cos(B) = 0.7071069751
arccos(cos(B)) = arccos(0.7071069751)
B = ???

Answer 38

just these last steps and you're done

Answer 39

your killing me man, your killing me haha

Answer 40

lol

what is `arccos(0.7071069751)` equal to ?

Answer 41

use a calculator like this one if you don't have a calculator with arccos

http://web2.0calc.com/

Answer 42

I got .7602444711?

Answer 43

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

Answer 44

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

Answer 45

round it up its 45. Cool

Answer 46

yeah 44.999984287488 ---> 45

Answer 47

awesome, Its correct. Thank you, alot

Answer 48

you're welcome

Answer 49

Means a lot ^-^

Answer 50

I'm glad to be of help

Answer 51

Yay! lol

Answer 52

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