Calculating Distance and Direction Between Two Teams in a Remote Area Using GPS

[jehan4141]

Two geological field teams are working in a remote area. A global positioning system (GPS) tracker at their base camp shows the location of the first team as 38 km away, 19° north of west, and the second team as 29 km away, 35° east of north. When the first team uses its GPS to check the position of the second team, what does the GPS give for the distance between the teams and direction,θ, measured from due east?

Homework Equations

F_x = Fa_x + Fb_x
F_y = Fa_y + Fb_y

Resultant vector = sqrt[ (F_x² + F_y² ]

Θ = tan^-1 (F_y/F_x)

The Attempt at a Solution

F_x = -38cos19 + 29cos55 = -19.29598922
F_y = 38sin19 + 29sin55 = 36.12699915

Resultant vector = sqrt [ (-19.29598922)² + (36.12699915)²]
Resultant vector = 40.95723706 meters

Θ = tan^-1(36.12699915/-19.29598922)
Θ = 61.89263517 degrees N of W

Those are my answers but apparently they are wrong. The provided answers are 53.8 km, 12.2 ° from east. Where am I going wrong? Thank you in advance :)

 

[lewando]

You determined A + B. I think you want B with respect to A. Draw a diagram of what is going on and you may see the solution.

 

[jehan4141]

Isn't A+B the distance between A and B?

 

[jehan4141]

I drew a diagram from the very beginning and still don't see my error.

 

[lewando]

Isn't A+B the distance between A and B?

No. It is a vector sum. I think you want a vector difference.