document.write( "Question 819430: [ An airplane, which has airspeed of 575 km/hr, heads directly east. The wind is blowing with a velocity of 82.0 km/hr on a heading of 35.0 degrees West of South. What will the resulting velocity of this airplane be as measured from the ground? The answer is: 532 km/hr at 7.25 degrees SE ] \n" ); document.write( "
Algebra.Com's Answer #493102 by TimothyLamb(4379)\"\" \"About 
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\n" ); document.write( "airplane vector a:
\n" ); document.write( "draw horizontal line (magnitude 575 kph) pointing to the right for east
\n" ); document.write( "---
\n" ); document.write( "wind vector b:
\n" ); document.write( "at the tip of vector a draw vector b (magnitude 82 kph) at 55 degrees below a (90 - 35 = 55)
\n" ); document.write( "call this angle C
\n" ); document.write( "---
\n" ); document.write( "the result vector c:
\n" ); document.write( "vectors a and b form two sides of a triangle, and the third side is vector c, the wind-corrected velocity of the airplane
\n" ); document.write( "---
\n" ); document.write( "to find the magnitude of vector c use the law of cosines: c^2 = a^2 + b^2 - 2ab*cos(C)
\n" ); document.write( "---
\n" ); document.write( "c^2 = a^2 + b^2 - 2ab*cos(C)
\n" ); document.write( "c^2 = 575^2 + 82^2 - 2(575)(82)*cos(55)
\n" ); document.write( "c = sqrt( 575^2 + 82^2 - 2(575)(82)*cos(55) )
\n" ); document.write( "c ~= 532.222 kph
\n" ); document.write( "---
\n" ); document.write( "to find the angle B between vector a and vector c use the law of sines: a/sin(A) = b/sin(B) = c/sin(C)
\n" ); document.write( "---
\n" ); document.write( "b/sin(B) = c/sin(C)
\n" ); document.write( "sin(B) = b*sin(C)/c
\n" ); document.write( "sin(B) = 82*sin(55)/532.222
\n" ); document.write( "B = arcsin( 82*sin(55)/532.222 )
\n" ); document.write( "B ~= 7.250 degrees
\n" ); document.write( "---
\n" ); document.write( "answer:
\n" ); document.write( "using proper aviation bearing terminology, and avoiding antiquated references such as SE, West of South, etc., the wind-corrected velocity of the airplane relative to the ground, is:
\n" ); document.write( "532 kph at 97.3 degrees true north
\n" ); document.write( "---
\n" ); document.write( "Solve and graph linear equations:
\n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php
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\n" ); document.write( "Solve quadratic equations, quadratic formula:
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\n" ); document.write( "Calculate and graph the linear regression of any data set:
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