SOLUTION: 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 b
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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? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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 =
Cross multiply
sin(65)*a = 29 * sin(55)
a =
a = 26.2 mi from B to the fire
and =
Cross multiply
sin(65)*b = 29 * sin(60)
b =
b = 27.7 mi from A to the fire
