Vector Components HW: Find Distance/Dir from Lake B to Base Camp

AI Thread Summary
To find the distance and direction from Lake B back to Base Camp, the plane's journey involves calculating vector components. The initial leg to Lake A is 280 km at 20 degrees north of east, yielding components of approximately 263 km east and 95.8 km north. The second leg to Lake B is 190 km at 30 degrees west of north, resulting in components of about 184.5 km west and -95 km south. The user struggles with summing the components correctly and is advised to double-check calculations, particularly for the cosine of -30 degrees, and to consider drawing a diagram for clarity. Accurate component addition is essential for determining the final vector from Lake B to Base Camp.
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Homework Statement



A plane flies from base camp to lake A, a distance of 280km, at a direction of 20 degrees north of east. After dropping thr supplies, it flies to lake B which is 190km and 30 degrees west of north from lake A. Determine the distance and direction gtom lake B to the base camp

Homework Equations


Axcos theta
Bysin theta

r= Sq rt (X^2 + y^2)

tan - theta = y/x


The Attempt at a Solution



280 cos 20 = 263
280 sin 20 = 95.8

190cos -30 = 184.5
190sin -30 = -95

I tried to add up the components but it doesn't end up being the rigth answer from the book.
 
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Perhaps recalculate those numbers. In particular what is 190*cos(-30)?
 
Did you draw a diagram? What did you get for the x and y components of the final vector?
 
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