document.write( "Question 1194112: A ship leaves a dock at 13 mph. After an hour it is seen from a lighthouse 12 miles east of the dock to bearing N12°30’W. How far is it from the lighthouse? What is its bearing from the dock? \n" ); document.write( "
Algebra.Com's Answer #826276 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Let the dock be at D, the lighthouse at L, and the ship at S.\r\n" );
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document.write( "A bearing of N12o30'W means this: \r\n" );
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document.write( "Think of starting by putting your elbow at L. Point your arm North (up), \r\n" );
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document.write( "then swing your arm toward the West (left) through an angle of 12o30'.  \r\n" );
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document.write( "Since 30' means half a degree, I will write the angle as 12.5o. \r\n" );
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document.write( "To find ∠DLS we subtract 90o-12.5o = 77.5o.\r\n" );
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document.write( "Since the ship travels at 13 mph, and travels 1 hour, the distance \r\n" );
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document.write( "DS = 13 miles, the distance from the dock.   \r\n" );
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document.write( "We find ∠S by using the law of sines:\r\n" );
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document.write( "\"12%2Fsin%28%22%3CS%22%5E%22%22%29\"\"%22%22=%22%22\"\"13%2Fsin%2877.5%5Eo%29\"\r\n" );
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document.write( "\"13%2Asin%28%22%3CS%22%5E%22%22%29\"\"%22%22=%22%22\"\"12%2Asin%2877.5%5Eo%29\"\r\n" );
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document.write( "\"sin%28%22%3CS%22%5E%22%22%29\"\"%22%22=%22%22\"\"12%2Asin%2877.5%5Eo%29%2F13\"\"%22%22=%22%22\"\"0.9011963143\"\r\n" );
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document.write( "∠S = 64.3157657o\r\n" );
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document.write( "Now we find ∠LDS by using the fact that the three angles of\r\n" );
document.write( "ΔDLS must have sum 180o.\r\n" );
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document.write( "∠LDS = 180o - 64.3157657o - 77.5o = 38.1842343o\r\n" );
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document.write( "To find the distance from the lighthouse to the ship, LS, we use the\r\n" );
document.write( "law of cosines:\r\n" );
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document.write( "\"LS%5E2\"\"%22%22=%22%22\"\"DS%5E2%2BDL%5E2-2%2ADS%2AFL%2Acos%28%22%3CLDS%22%29\"\r\n" );
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document.write( "\"LS%5E2\"\"%22%22=%22%22\"\"13%5E2%2B12%5E2-2%2A13%2A12%2Acos%2838.1842343%5Eo%29\"\r\n" );
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document.write( "\"LS\"\"%22%22=%22%22\"\"8.231619989\"miles.\r\n" );
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document.write( "That's the first thing you were asked for.\r\n" );
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document.write( "To get the bearing angle from D, we subtract ∠LDS from 90o\r\n" );
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document.write( "90o - 38.1842343o = 51.8157657o\r\n" );
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document.write( "For the bearing from D, think of starting by putting your elbow at D. \r\n" );
document.write( "Point your arm North (up), then swing your arm toward the East (right) \r\n" );
document.write( "through an angle of 51.8157657o.\r\n" );
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document.write( "Since the first bearing was given in degrees and minutes, we change\r\n" );
document.write( "the decimal part to minutes by multiplying by 60':\r\n" );
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document.write( "(0.8157657)(60') = 48.945942' which we round to 49'\r\n" );
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document.write( "So the bearing from D is N51o49'E.\r\n" );
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document.write( "Edwin
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