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 6000 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 5050 feet from the first tower, and 2420 feet from the second. Determine your position north and east of the first tower, \thetaθ, to the nearest tenth of a degree.
Point A is where you're standing. Point B is the first tower. Point C is the second tower.
First let's find angle B using the law of cosines.
24202 = 50502 + 60002 - (2)(5050)(6000)(cosB)
5856400 = 61502500 - 60600000cosB
-55646100/-60600000 = cosB
0.91825 ≈ cosB
B ≈ 23.328°
So the angle that I think the problem is asking for is approximately 23.3°.
Next we can find x.
0.91825 ≈ x/5050
x ≈ 4637.163
So the position east of the tower is approximately 4,637.2 feet
Next we can find y.
0.39599 ≈ y/5050
y ≈ 1999.771
So the position north of the tower is approximately 1,999.8 feet.