The distance between two locations, a and b, is calculated using a third location c at a distance of 15 miles from location b. if ∠b = 105° and ∠c = 20°, what is the distance, to the nearest tenth of a mile, between locations a and b? a) 42.4 miles b) 35.9 miles c) 6.3 miles d) 5.3 miles

First find ∠A: ∠A = 180°-(105°+20°) = 180°-125° = 55°
Make sure you know the Law of Sin (or Sin Law):
15/sin 55° = AB/sin 20°, then 15 / 0.81915 = AB/0.342
AB(0.81915) = 15(0.342)
AB(0.81915) = 5.13
AB = 5.13 : 0.81915 (ratio)
AB = 6.26 = 6.3 miles
Therefore, the distance between location A and location B is 6.3 miles.