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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 44 km away, 25degree north of west, and the second team as 29 km away, 36degree 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? (a) Number Units (b) Number Units

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(a) You can use the law of cosines to determine the distance.

Distance from base camp to first team = a = 44 km

Distance from base camp to second team = b = 29 km

Angle at base camp between the teams = C = 90 - 25 + 36 =101 deg

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 44^2 + 29^2 - 2*44*29*cos(101)

c^2 = 1936 + 841 - 2552*(-0.191)

c^2 = 3264.43

c = 57.14 km

(b) If we calculate the angle at the first base camp using the triangle from above we can then get the angle as measured from due east of the second camp by subtracting 25 degrees from it.

sin(C)/c = sin(B)/b

sin(B) = (b/c)sin(C) = (29/57.14)*0.982 = 0.498

B = 29.89 degrees

So the angle as measured from due east of camp 2 from camp 1 will be 29.89 degrees.

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