SOLUTION: Two fire look-out stations are 20 miles apart with station B directly east of station A. Both stations spot a fire. The bearing of the from station A is {{{matrix(1,3,N,"35°",E)}}}

Draw the picture. 

The bearing  at A means:
Start by pointing North at A, which is straight upward, 
then from there swing 35° toward the East, which is
clockwise. 

The bearing  at B means: 
Start by pointing North at B, which is straight upward, 
then from there swing 49° toward the West, which is
counter-clockwise. 

Label the unknown distance to be found from A to the 
fire as x:



The two angles at A are complementary, so the angle inside the triangle
at A is 90°-35° or 55°.  So label that one 55°.

The two angles at B are also complementary, so the angle inside the triangle
at B is 90°-49° or 41°.  So label that one 41°.



Now erase everything but just the triangle and its interior angles
and the sides:



Since the sum of all three angles of a triangle is 180°, we can calculate
the angle at the FIRE, by adding the two angles 55°+41°, getting 96°, and
then subtracting that from 180° getting 84°. So label the angle at the
FIRE 84°:



The law of sines tells us that the ratio of any side to its opposite
angle's sine is equal to the ratio of any other side to its opposite
angle's sine.  

The angle opposite x is 41° and the angle opposite 20 is 84°. So,

x is to sin(41°) as 20 is to sin(84°) or



Cross multiplying:

 

Solve for x by dividing both sides by 



Get your calculator:





So the answer nearest that is 13 miles.

Edwin