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On many cell phones with GPS, an approximate location can be given before the GPS signal is received. This is done by a process called triangulation, which works by using the distance from two known points. Suppose there are two cell phone towers within range of you, located 3000 feet apart along a straight highway that runs east to west, and you know you are north of the highway. Based on the signal delay, it can be determined you are 2050 feet from the first tower, and 1420 feet from the second. Determine the angle, \theta θ , between your line of sight to the first tower and the highway to the nearest tenth of a degree. (A calculator is needed for this question)

 Mar 9, 2020
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Law of cosines

 

a^2 + b^2 - 2ab cos(theta) = c^2

2050^2 + 3000^2 - 2 (2050)(3000)cos (theta) = 1420^2      theta in this will be the angle between the highway and your line of sight to the first tower

                                                                                                  in a right triangle....the angle you want is 180-90-theta

 

theta = 24.57

 

180-90-24.57  = 65.4o

 Mar 9, 2020

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