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?

We will first calculate ∠A:

∠∠A = 180° - (105° + 20 °) = 180° - 125° = 55°

Then we will use the Sine Law:

15 / sin 55° = AB / sin 20°

15 / 0.81915 = AB / 0.342

AB · 0.81915 = 15 · 0.342

AB · 0.81915 = 5.13

AB = 5.13 : 0.81915

AB = 6.26 ≈ 6.3 miles

Answer: The distance between the locations A and B is 6.3 miles.