Question

find the measure of MN to the nearest tenth using the law of cosines.

Answer 1

is there some sort of formula

Answer 2

because i know that if you add all the angels it has to equal 180 to be a right triangle

Answer 3

Law of Cosines relates the cosine of each angle to the side lengths
of the triangle. it can be either
\[a^2=b^2+c^2=2bccosA\]
\[b^2=a^2+c^2-2accosB\]
\[c^2=a^2+b^2-2abcosC\]

those are the formulas I was given...

Answer 4

@thomaster

Answer 5

MN^2 = ML^2 + LN^2 - 2(ML)(LN)cos104

Answer 6

how ^^

Answer 7

so,
MN^2 = (48)^2 + (29)^2 - 2(48)(29)cos104
simplify then take the square root to get MN

Answer 8

can you explain it a little more

Answer 9

I don't understand how to do this

Answer 10

@thomaster

Answer 11

This is a Law of Cosines problem

Answer 12

yes how the heck do I do law of cosines....@phi

Answer 13

The Law of Cosines says if you want to find the length of side c, then you need the angle opposite that side (often called C), and the two sides

Answer 14

to do you your problem, you need to find side MN

what is the angle opposite side MN ?

Answer 15

<L

Answer 16

= 104º
which we will call C (to match the formula)
we also need the other two sides,which we call a and b

they give us the other 2 sides. we can call one a and the other b (which is which does not matter for the formula)

so let a= 48 and b= 29

we are ready!
write down the formula

\[ c^2 = a^2 + b^2 - 2\ a\ b\ \cos(C) \]
replace the letters a, b and C with the numbers from the problem
can you do that ?

Answer 17

\[104^2=48^2+29^2-2(48)(29) \cos 104\]



like that??

Answer 18

exactly like that.

except the left side is not 104^2 that is lower case c, representing the length of the side opposite the angle 104º

so you have
\[ c^2 = 48^2+29^2−2(48)(29)\cos104 \]

Answer 19

now do the arithmetic on the right side to find c^2

take the square root to find c
which is the side MN for this problem.

Answer 20

oh my mistake......what do we do next

Answer 21

get out your calculator and figure out what the right side is

Answer 22

do I do -2(48)*(29)

Answer 23

i got a negative number....

Answer 24

you do what it says
\[ c^2 = 48^2+29^2−2(48)(29)\cos104 \]
that means find
48*48
add that to
29*29

add that to -2 * 48* 29 * cos(104)

Answer 25

can you do -2*48*29*cos(104) ?

or you can do it using google: type into google
48^2 + 29^2 - 2*48*29*cos(104 degrees)=

but I would learn how to get the same number using a calculator

Answer 26

3818.51055735

Answer 27

that's what popped up

Answer 28

yes, that means
c^2 = 3818.51055735

see if you can get the same number using your calculator.

now to find c, take the square root of both sides
sqr(c^2) is c
sqr(3818.51055735) = 61.794098

c= 61.794098

find the measure of MN to the nearest tenth
now round to the nearest tenth

Answer 29

61.8

Answer 30

ty @phi