Question

An obtuse triangle with area 12 has two sides of lengths 4 and 10. Find the length of the third side. (There are two answers.) (Use law of cosines)

Answer 1

I got up to the law of cosines

Answer 2

do you know the law of cosines?

Answer 3

yeah I did the law of cosines and I ended up getting 1.45=cos4/5

Answer 4

you know about arccosine?

Answer 5

that's where you will get two answers

Answer 6

nope what is that

Answer 7

Oh yeah I know this is a two answer problem

Answer 8

arccosine is the function that undoes cosine

Answer 9

it's probably on your calculator as \[\cos^{-1} \]

Answer 10

yeah I have that, but do i divide 1.45 by 4/5 to get cos by itself then take the inverse?

Answer 11

no, cos (4/5) can't be split like that

Answer 12

so did I do it wrong?

Answer 13

let's start from the beginning of the problem.

Answer 14

okay, so i made a triangle, and I found cos by doing 12=(1/2)(10)(4sinC) and that is how I got cos=+-4/5

Answer 15

Then I did the law of cosines

Answer 16

ok... that's confusing.
law of cosines has nothing to do with the area of the triangle.

Answer 17

Well the area of the triangle was given, so I'm trying to find the third side of the triangle idk I'm so confused

Answer 18

Apparently the overall answers are 13.4 and 7.21

Answer 19

"okay, so i made a triangle, and I found cos by doing 12=(1/2)(10)(4sinC) and that is how I got cos=+-4/5"

Answer 20

that step would give you sinC, did you use sin^2 + cos^2 =1 to get cos?

Answer 21

no

Answer 22

how did you get cos from sin?

Answer 23

i have no idea i looked at someones paper

Answer 24

don't do that. it makes things harder sometimes.

Answer 25

okay so how do I get the answer to this problem?

Answer 26

you can use sin^2 C + cos^2 C =1 to get cos C

Answer 27

or you could use arcsine to find angle C

Answer 28

what would sin=

Answer 29

12=(1/2)(10)(4sinC)

Answer 30

12=20 sin C
sin C= 12/20=6/10=3/5

Answer 31

yes i have that

Answer 32

but where do i go from there??