Finding missing side of a non right triangle

[coooool222]

QUESTION 22: Find length c

I’m getting 5.333 but it’s not in the answer choices.
I using the law of cosines please help

Work:
c^2 = (4/3)^2 + 4^2 -2(4/3)(4) cos C
c^2= 16/9 + 16 -32/3 (-1/2)
c^2 = 256/9
= sqrt 416/18
= 4.807

 

[JeffM]

I do not see where you got 4 and 4/3 in the first place. Perhaps I am being stupid.

Nor do you label your unknowns.

I’d start by calculating all the angles and then using the law of sines.

 

[lev888]

I do not see where you got 4 and 4/3 in the first place. Perhaps I am being stupid.

Nor do you label your unknowns.

I’d start by calculating all the angles and then using the law of sines.

It's given that b=3a=4

 

[JeffM]

It's given that b=3a=4

Duh. I was looking at 24.

 

[blamocur]

I get a different answer, but it is not among the listed multiple choices either.

 

[lev888]

QUESTION 22: Find length c

I’m getting 5.333 but it’s not in the answer choices.
I using the law of cosines please help

Work:
c^2 = (4/3)^2 + 4^2 -2(4/3)(4) cos C
c^2= 16/9 + 16 -32/3 (-1/2)
c^2 = 256/9
= sqrt 256/9
= 5.33333

I am not getting c^2 = 256/9.

 

[coooool222]

It's given that b=3a=4

 

[coooool222]

Whoops I mean c^2 = 416/18

 

[coooool222]

Noo how do I unsolve

 

[Steven G]

How do you solve c^2 = 416/18?

Well c^2 = 416/18 = 208/9. So c = sqrt(208)/sqrt(9) = sqrt(16)*sqrt(13)/sqrt(9) =.....

 

[Dr.Peterson]

QUESTION 22: Find length c

I’m getting 5.333 but it’s not in the answer choices.
I using the law of cosines please help

Work:
c^2 = (4/3)^2 + 4^2 -2(4/3)(4) cos C
c^2= 16/9 + 16 -32/3 (-1/2)
c^2 = 256/9
= sqrt 416/18
= 4.807

View attachment 33039

Could it be a typo, and they meant this?

​

That was my immediate impression, because what they wrote is a little weird.

 

[coooool222]

Could it be a typo, and they meant this?

View attachment 33042​

That was my immediate impression, because what they wrote is a little weird.

You are right I did the math and it’s sqrt 37