Determine the distance from the fire to B.

Question

Lookout station B is located 5 mi due east of station A.  The bearing of a fire from A is S 9°20ʹW and the bearing
from B is S32°40ʹW. Determine the distance from the fire to B (to the nearest tenth of a mile). What formula would you use?

Answer 1

Picture the triangle formed by joining points A, B, F where point F is the location of the fire. Draw a diagram.

The m∠A = 99º20' (add the 90º formed by vertical South and horizontal East to the 9º20' West of South).

The m∠B = 57º20' (subtract 32º40' from 90º)

The m∠F = 180 - (99º20' + 57º20') = 23º20'

We found the measure of ∠F because we know the length of the side opposite that angle, which is 5.That means we can use the Law of Sines to find BF.

BF/sin(99º20') = 5/sin(23º20')

BF = 5sin(99º20')/sin(23º20')

Since 1º = 60', 20' = 20/60 º = 1/3 º

If you are using a calculator to determine BF:

BF = 5sin(99 + 1/3)/sin(23 + 1/3) ≈ 12.5 miles

desmos.com/calculator/nqtacsykk8