SOLUTION: Police can use the pings from cell phone towers when a cell phone call is being used to triangulate a phones user location if they know the location of the two towers and the dista

Question 935899: Police can use the pings from cell phone towers when a cell phone call is being used to triangulate a phones user location if they know the location of the two towers and the distance between them. Murphy the mouth robbed the Second National Bank Of Carthage and Dropped out of site ... Until his girlfriend used the phone to call her mother police cars are waiting near each cell tower.

If the Cell Phone towers are 12,753 feet apart and the angle from one towers to the phone is 68 degrees and from the other tower to the phone is 53 degrees, determine the distances CT and TH to the nearest tenth of a mile. Will the police cars at the point C or point H arrive at the hideout first if they travel at the same speed?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
find the third angle:
180 - 68 - 53 = 59 degrees
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CT:
use law of sines:
a/sinA = c/sinC
a/sin(68) = 12753/sin(59)
a = sin(68)*12753/sin(59)
a = 13794.7115897 feet
a = 13794.7115897 feet * (1/5280 mile/feet)
a = 2.61263477078
CT = 2.6 miles
---
TH:
use law of sines:
b/sinB = c/sinC
b/sin(53) = 12753/sin(59)
b = sin(53)*12753/sin(59)
b = 11882.1595869 feet
b = 11882.1595869 feet * (1/5280 mile/feet)
b = 2.25040901267
TH = 2.3 miles
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the police car at H will arrive first
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