Question

Find the angles

Diagram below!

Answer 1

do you know the different relationships between the sides and the angles of triangles?

Answer 2

so we have an isosceles triangle since two sides are 11

Answer 3

Yes that means two of the angles will be the same, correct?

Answer 4

yes! i was about to right that

Answer 5

that's one info that can help us
let's call that angle x
and the other angle y
so 2x+y=180

Answer 6

next is to use law of sine as my instincts tell me hehehe

Answer 7

Well that's the hard part for me

I just learned law of cosine (so bad at it) and haven't learned law of sine yet >.<

Answer 8

eh law of cosine could also be good! hehe
let's try it!

Answer 9

Okay! :) Thank you by the way >.<

Answer 10

\[14^2=11^2+11^2-2(11)(11)\cos y\]

Answer 11

that's one part

Answer 12

Okay so,

196=121+121-2(121)cosy?

Answer 13

let's rearrange it
\[14^2=2(121)(1-\cos y) \Longrightarrow \cos y=1-\frac{196}{242}\]

Answer 14

Or, we could do that xD that makes more sense

Answer 15

taking another equation
\[11^2=14^2+11^2-2(14)(11)\cos x \Longrightarrow \cos x=\frac{196}{308}\]

Answer 16

hmm let's see now how can we find the angles

Answer 17

Are you asking me? >.<

Answer 18

hmm im thinking lol

Answer 19

Because all I know is using the law of cosine equations

Answer 20

c2 = a2 + b2 − 2ab cos(C)

Answer 21

that's what i did above hehe

Answer 22

Oh wait so Cos c= cos x?

Answer 23

Shouldn't it be

C=Cos^-1(196/308) then?

Answer 24

Just a guess >.< maybe I'm wrong

Answer 25

hmm i guess that's a good way to go at it hehe

Answer 26

I'm right ._. ?

Answer 27

haha you naturally attempt that, but i think that is not the purpose here

Answer 28

see what you find and tell me the values

Answer 29

Okay currently calculating!

Answer 30

weird the calculator I use online doesn't give me an answer ._.

Answer 31

i tried it won't give you the right answer lol

Answer 32

It just gives me a different equation

Answer 33

wait I got uhm
0.88102

Answer 34

https://www.symbolab.com/solver/trigonometric-equation-calculator/Cos%5E%7B-1%7D%5Cleft(196%2F308%5Cright)/?origin=button

Answer 35

no forget that heeh

Answer 36

two of the angles are evidently the same

Answer 37

i'm not even thinking lol!
@satellite73 we have deduced that thus far lol

Answer 38

this supposed to be solved two equation involving x and that was my initial feeling

Answer 39

really you should use this
\[\cos(Y)=\frac{11^2+11^2-14^2}{2\times 11\times 11}\]

Answer 40

usually these are done in degrees

Answer 41

that is what we are doing hehe
i guess we missed something in the calculatiions

Answer 42

\[Y=\cos^{-1}(\frac{23}{121})\]

Answer 43

because i did that in the sum of those angle an they are not 180

Answer 44

it is possibly bad math hehe

Answer 45

about \(79.04^\circ\)
http://www.wolframalpha.com/input/?i=arccos%2823%2F121%29

Answer 46

eh you got the point!
do it in the calculator :)

Answer 47

Okay wait so the biggest angle is 79.04?

And the other two anges is 100.96/2?

Answer 48

it is just some math error

Answer 49

angles*

Answer 50

yeah should be

Answer 51

2x+y=180
2x=180-79.04 and you get that answer

Answer 52

50.98

Answer 53

i was thinking of something else hehe

Answer 54

yeah sounds good

Answer 55

Mind helping me with one more @xapproachesinfinity ?

Answer 56

hehe not in the mood! let's see the problem