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**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

_{x}

^{2}+ F

_{y}

^{2}]

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 :)