Question

Lookout station B is located 9 mi due east of station A. The bearing of a fire from A is S 19W and the bearing from B is S 39.833W. How do you determine the distance from the fire to B (to the nearest tenth of a mile)?

Answer 1

Distance to Fire from station B: `color(green)(29.9" miles")`

Explanation:

Here is my understanding of the situation:

`/_FAB= 19^@+90^@=109^@`
`/_ABF = 90^@-39.833^@`
`/_AFB = 180^@ - (/_FAB+/_ABF) = 20.837^@`

By the Law of Sines:
`abs(FB)/(sin(/_FAB))=abs(AB)/(sin(/_AFB))`

`abs(FB)= (9" miles")/(sin(20.837^@)) xx sin(109^@)`

and with the aid of a calculator:
`abs(FB)~~29.923" miles"`