SOLUTION: A ranger in fire tower A spots a fire at a direction of 40�. A ranger in fire tower B, which is 28 miles directly east of tower A, spots the same fire at a direction of 50�. How

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Question 267158: A ranger in fire tower A spots a fire at a direction of 40�. A ranger in fire tower B, which is 28 miles directly east of tower A, spots the same fire at a direction of 50�. How far from tower B is the fire?
Answer by stanbon(75887) (Show Source):
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A ranger in fire tower A spots a fire at a direction of 40�.
A ranger in fire tower B, which is 28 miles directly east of tower A, spots the same fire at a direction of 50�.
How far from tower B is the fire?
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Draw the figure. Let the fire be at point F
angle A = 40 degrees
angle B = 180-58 = 122 degrees
angle F = 180-(40+122) = 18 degrees
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Use Law of Sines:
a/sin(40) = 28/sin(18)
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a = sin40[28/sin(18)]
a = 58.25 miles
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Cheers,
Stan H.