Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35��E from the western station and on a bearing of N 23��E from the eastern station. How far is the balloon from the western station?

There is a picture but I am unable to attach its file :/ For the answer i kept getting 141 but it appears in the picture that the 146 side is way smaller and the 141 i am getting is way longer than that appropriating side ( this is a Essay question )

Question

Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35��E from the western station and on a bearing of N 23��E from the eastern station. How far is the balloon from the western station?

There is a picture but I am unable to attach its file :/ For the answer i kept getting 141 but it appears in the picture that the 146 side is way smaller and the 141 i am getting is way longer than that appropriating side ( this is a Essay question )

anonymous · Answer

@DangerousJesse

anonymous · Answer

@Hero

anonymous · Answer

here is my work for the problem, : 

Distance between two points W and E = 146 miles and B is the position of B (balloon) 
Angle BWE =55 degrees and angle BEW =67 degrees
therefore angle WBE = 180-55-67 =58 degrees 
Using sine formula 
w/sin(55)= b/sin(58) 
w= 146{sin 55/ sin 58) =
141 miles

anonymous · Answer

did I do this correctly?

anonymous · Answer

@iambatman @Ashleyisakitty

anonymous · Answer

@nincompoop

dangerousjesse · Answer

I'm going to use the same variables, BWEN= Balloon, West, East, North. 
The paragraph has already told us that $\textsf{east->west=146.}$ 
It told us that the line made by B and W = a 38 degree angle with the N direction.
N is also perpendicular with the line made by W and E
$\textsf{angle BWE}$ is $90-38=52.$ 
The line from E to B makes a 17 degree with the northern direction so $\textsf{BEW = 90+17 = 107}$. It follows that the angle $WBE = 180-52-107=21$. 
$\frac{WB}{sin  \;107} = \frac{WE}{sin\; 21}$ 
We already know that $\textsf{WE=146}$ and WB=$\frac{ sin \;107}{sin\; 21} = 389.6 \textsf{ miles} $

dangerousjesse · Answer

Sorry for taking so long, I got distracted.

anonymous · Answer

did you get north as in a 2nd triangle?

anonymous · Answer

wait so the answer is 389.6?

dangerousjesse · Answer

No, north wasn't a separate triangle. Yes, I got 390

anonymous · Answer

I was just wondering how North was added in. Because you said you used the same variables. the balloon,east and west. the north entry is what confused me

dangerousjesse · Answer

I just used it as a perpendicular angle to west and east.

anonymous · Answer

oooo... That makes a little bit more sense. Thank you ^_^