SOLUTION: An airplanes flies from city A to city B, a distance of 150 miles, and then turns through an angle of 30 degrees and heads towards city C. If the distance between A and C is 360 mi

Question 934731: An airplanes flies from city A to city B, a distance of 150 miles, and then turns through an angle of 30 degrees and heads towards city C. If the distance between A and C is 360 miles, how far is it from city B to C? Through what angle should the pilot turn at city C to return to city A? The distance from city B to C is approx.?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
turning angle of 30 degrees = included angle of (180 - 30) = 150 degrees
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law of sines:
sin( C degrees )/150 miles = sin( 150 degrees )/360 miles
sin( C degrees ) = 150 miles * sin( 150 degrees )/360 miles
sin( C degrees ) = 150 miles * 0.5/360 miles
sin( C degrees ) = 150 * 0.5/360
sin( C degrees ) = 0.208333333333
C = inverse-sin( 0.208333333333 )
C = 12.0247 degrees
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internal angles add to 180 degrees:
30 + 12.0247 + A = 180
A = 180 - (30 + 12.0247)
A = 137.9753 degrees
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law of sines:
sin( A degrees )/a = sin( 150 degrees )/360 miles
sin( 137.9753 degrees )/a = sin( 150 degrees )/360 miles
a = sin( 137.9753 degrees ) * 360 miles / sin( 150 degrees )
a = sin( 137.9753 ) * 360 miles / sin( 150 )
a = 482.005 miles
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answer:
angle pilot turns at city C to return to city A is approximately = 12 degrees
distance from city B to C is approximately = 482 miles
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