Two geological field teams are working in a remote area. A global positioning sy

Question

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 39 km away, 17° north of west, and the second team as 26 km away, 38° 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?

I got 54 km for a), which is right, and I got 26.7 degree for b), which is wrong.......and I have tried to calculate for a few times....it's still 26.7...maybe I am not understanding the question right..if anyone can provide a diagram and detailed explanation would be the best. Thank you!

Explanation / Answer

Draw a picture making each vector the hypotenuse of a right triangle with the legs going East-West and North-South.

Decompose each of the original vectors into ordered pairs, using East as the positive x direction and North as the positive y. The lengths of the legs of the right triangles are computed using the sine and cosine of the given angle.

V1 = (-40 * cos(17), 40 * sin(17))

V2 = ( 26 * cos(35), 26 * sin(35))

To travel from the first team to the second team, you reverse V1 to get back to the base camp and the follow v2. This will give the resultant vector.

Vr = -V1 + V2

= (40 * cos(17) + 26 * cos(35), -40 * sin(17) + 26 * sin(35))

= (59.6, 3.22)

The distance is the magnitude of the Vr.

d = sqrt(59.6^2 + 3.22^s) = 59.7

To compute the angle, use the tangent of the North component divided by the East component.

angle = arctan(3.22 / 59.6) = arctan(0.054) = 3.09 degrees.

Looking at the picture, we can see the angle is Nort of East.

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