document.write( "Question 1196965: Lookouts on two naval vessels, about 2 miles apart, spot a disabled boat off the port side. One lookout spots the boat at an angle of 42° with the line connecting the naval vessels. The other lookout spots the boat at an angle of 28° with the same line. \r
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Algebra.Com's Answer #830033 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Lookouts on two naval vessels, about 2 miles apart, spot a disabled boat off the port side.
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document.write( "You have a triangle ABC, where A is the point of the first lookout and B is the point \r\n" );
document.write( "of the second lookout. The point C is where the disable boat is located.\r\n" );
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document.write( "Answer to (a) is easy: in any triangle, the longer the side is, the greater is the opposite angle.\r\n" );
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document.write( "In our case, angle at A is 42°, while angle at B is 28°.\r\n" );
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document.write( "Since angle A is greater than angle B, it means that side BC is longer than side AB.\r\n" );
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document.write( "Thus, vessel A is closer to the disable boat than vessel B.    It is the ANSWER to question (a)\r\n" );
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document.write( "To solve (b), use the sine law\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "We know c = 2 kilometers, C = 180° - 42° - 28 = 110°. \r\n" );
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document.write( "So,   =  =  = 2.12836  (rounded).\r\n" );
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document.write( "Therefore,  a = 2.12836*sin(A) = 2.12836*sin(42°) = 2.12836*0.66913 = 1.424 kilometers,\r\n" );
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document.write( "            b = 2.12836*sin(B) = 2.12836*sin(28°) = 2.12836*0.46947 = 0.999 kilometers.\r\n" );
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document.write( "Thus  A  is closer than  B  by  a - b = 1.424 - 0.999 = 0.425 kilometers = 425 meters, approximately.\r\n" );
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