Physics

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 41 km away, 24° north of west, and the second team as 33 km away, 37° east of north. When the first team uses its GPS to check the position of the second team, what does it give for the second team's (a) distance from them and (b) direction, measured from due east?

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  1. α=(90-24)+ 37=103⁰
    Cosine law:
    d=sqrt{ 41²+33²-2•41•33•cos103⁰}=58 km
    Sine law:
    33/sinβ=58/sin α
    sinβ= sin α•33/58=0.554
    β=sin⁻¹0.554=33.7⁰
    angle=33.7⁰-24⁰=9.7⁰ (north of east)

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