document.write( "Question 1125459: Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second is sqrt 3 over 2, and if the second boat travels at 18km/h, how far apart, in km, are they at the end of 5 hours? \n" ); document.write( "
Algebra.Com's Answer #741825 by MathTherapy(10551)\"\" \"About 
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Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second is sqrt 3 over 2, and if the second boat travels at 18km/h, how far apart, in km, are they at the end of 5 hours?
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Let speed of 1st boat be S
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document.write( "Then we get the following: \"matrix%281%2C3%2C+18%2FS%2C+%22=%22%2C+2%2Fsqrt%283%29%29\"
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document.write( "\"matrix%281%2C3%2C+2S%2C+%22=%22%2C+18sqrt%283%29%29\" ------- Cross-multiplying
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document.write( "S, or speed of 1st boat = \"matrix%281%2C3%2C+18sqrt%283%29%2F2%2C+%22=%22%2C+9sqrt%283%29%29\"
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document.write( "We then get: 	Distance traveled by 1st boat in 5 hours: 
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document.write( "               \"matrix%281%2C4%2C+5%289%29sqrt%283%29%2C+%22=%22%2C+45sqrt%283%29%2C+km%29\"
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document.write( "Distance traveled by 2nd boat in 5 hours: 5(18) = 90 km\r
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document.write( "The side opposite the 30o angle represents the distance between the boats after 5 hours
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document.write( "Therefore, with 2 SIDES and an INCLUDED ANGLE (SAS), we use the law of cosines.
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document.write( "Let the side opposite the 30o angle (A) be a
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document.write( "Then we get: \"matrix%281%2C3%2C+a%5E2%2C+%22=%22%2C+b%5E2+%2B+c%5E2+-+2bc+Cos+%28A%29%29\"  
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document.write( "             \"matrix%281%2C3%2C+a%5E2%2C+%22=%22%2C+3%2845%29%5E2+%2B+90%5E2+-+90%2845%29%283%29%29\"
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document.write( "             \"matrix%281%2C3%2C+a%5E2%2C+%22=%22%2C+%222%2C025%22%29\"
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document.write( "             Distance the boats are apart, or 
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document.write( "             OR
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document.write( "             \"matrix%281%2C3%2C+a%5E2%2C+%22=%22%2C+b%5E2+%2B+c%5E2+-+2bc+Cos+%28A%29%29\"  
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document.write( "             Distance the boats are apart, or  \n" );
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