Question 1180189
two​ fire-lookout stations are 29 miles ​apart, with station B directly east of station A.
 Both stations spot a fire. 
 The bearing of the fire from station A is N35°E and 
 the bearing of the fire from station B is N30°W.
 How​ far, to the nearest tenth of a​ mile, is the fire from each lookout​ station?
:
Draw this out. Triangle ABC, where C is the point of the fire
The line from A to B is horizontal to the the north-south lines so the interior angle of of the triangle:
A = 90-35 = 55 degrees
B = 90-30 = 60 degrees
C = 180-55-60 = 65 degrees
:
label sides opposite the angles a, b, c
Use the law of sine
{{{a/sin(55)}}} = {{{29/sin(65)}}}
Cross multiply
sin(65)*a = 29 * sin(55)
a = {{{23.7554/sin(65)}}}
a = 26.2 mi from B to the fire
and 
{{{b/sin(60)}}} = {{{29/sin(65)}}}
Cross multiply
sin(65)*b = 29 * sin(60)
b = {{{25.1147/sin(65)}}}
b = 27.7 mi from A to the fire