Physics
steph
2016-09-26 00:53:09
A Texas rancher wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure below, where A = 4.90 km and θC = 15°.
ANSWERS
mzcutepie161
2016-09-26 07:39:54

the answer: the full question is as follow:  A Texas rancher wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in Figure below , where A = 4.90 km and θC = 15°. He then correctly calculates the length and orientation of the fourth side D. What is the magnitude and direction of vector D?  As shown in the figure,  A + B + C + D = 0, so to find the magnitude and direction of vector D, we should follow the following method:  D = 0 - (A + B + C) ,  let  W = - (A + B + C), so the magnitude and direction of vector D is the same of the vector W characteristics Magnitude  A + B + C =  (4.90cos7.5 - 2.48sin16 - 3.02cos15)I + (-4.9sin7.5 + 2.48cos16 + 3.02sin15)J = 1.25I +2.53J the magnitude of W= abs value of (A + B + C) = sqrt (1.25² + 2.53²) = 2.82   the direction of D can be found by using Dx and Dy value we know that     tanθo = Dx / Dy = 1.25 / 2.53 =0.49 tanθo =0.49 it implies θo = arctan 0.49 = 26.02° direction is 26.02°

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