document.write( "Question 30695: an airplane has an airspeed of 500 kilometers per hour in a northerly direction. the wind is 60 kilometers per hour in a south easterly direction. Find the actual speed and dircetion of the plane relative to the ground. \n" ); document.write( "

Algebra.Com's Answer #17416 by Paul(988) $\"\"$ $\"About$

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I am hoping that south easterly means SSE --> South south east which means that it has a bearing of 45 degrees.
\n" ); document.write( "North to east is 90 degress so 90+45=135degrees
\n" ); document.write( "In vector form this forms a oblique triangle:
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document.write( "N
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document.write( "|500km/h
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document.write( "|135 degrees 
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document.write( "   \60km/h
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document.write( "This allows us to use the cosine law:
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document.write( "Letting the unknow be in vector form of ||v+w||
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document.write( "Form cosine law: 
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document.write( "||v+w||≈ 544
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document.write( "TO find direction use sine law:
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document.write( "x ≈ 66\r
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document.write( "Hence, the ground speed of the plane is 544km/h making a direction of 66 degrees.
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document.write( "Paul.\r
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