Question

A forestal station receives the locations of two fires, one of them in a forest located 11 Km heading N69°W from the station. The second fire in a forest 21 Km heading S35°E. Calculate the distance on straight line between the two fires. Round your answer to one decimal place.

Answer 1

30.7 km

Explanation:

The distance between the two fires can be found using the Law of Cosines. For ΔABC in which sides 'a' and 'b' are given, along with angle C, the third side is ...

c = √(a² +b² -2ab·cos(C))

The angle measured between the two fires is ...

180° -(69° -35°) = 146°

and the distance is ...

c = √(11² +21² -2(11)(21)cos(146°)) ≈ √945.015

c ≈ 30.74

The straight-line distance between the two fires is about 30.7 km.