document.write( "Question 160624: Two fire look-out stations are 20 miles apart with station B directly east of station A. Both stations spot a fire. The bearing of the from station A is $\"matrix%281%2C3%2CN%2C%2235%B0%22%2CE%29\"$ and the bearing of the fire from station B is $\"matrix%281%2C3%2CN%2C%2249%B0%22%2CW%29\"$ . How far is it from station A to the fire?\r
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Algebra.Com's Answer #118447 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Draw the picture. \r\n" );
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document.write( "The bearing  at A means:\r\n" );
document.write( "Start by pointing North at A, which is straight upward, \r\n" );
document.write( "then from there swing 35° toward the East, which is\r\n" );
document.write( "clockwise. \r\n" );
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document.write( "The bearing  at B means: \r\n" );
document.write( "Start by pointing North at B, which is straight upward, \r\n" );
document.write( "then from there swing 49° toward the West, which is\r\n" );
document.write( "counter-clockwise. \r\n" );
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document.write( "Label the unknown distance to be found from A to the \r\n" );
document.write( "fire as x:\r\n" );
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document.write( "The two angles at A are complementary, so the angle inside the triangle\r\n" );
document.write( "at A is 90°-35° or 55°.  So label that one 55°.\r\n" );
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document.write( "The two angles at B are also complementary, so the angle inside the triangle\r\n" );
document.write( "at B is 90°-49° or 41°.  So label that one 41°.\r\n" );
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document.write( "Now erase everything but just the triangle and its interior angles\r\n" );
document.write( "and the sides:\r\n" );
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document.write( "Since the sum of all three angles of a triangle is 180°, we can calculate\r\n" );
document.write( "the angle at the FIRE, by adding the two angles 55°+41°, getting 96°, and\r\n" );
document.write( "then subtracting that from 180° getting 84°. So label the angle at the\r\n" );
document.write( "FIRE 84°:\r\n" );
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document.write( "The law of sines tells us that the ratio of any side to its opposite\r\n" );
document.write( "angle's sine is equal to the ratio of any other side to its opposite\r\n" );
document.write( "angle's sine.  \r\n" );
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document.write( "The angle opposite x is 41° and the angle opposite 20 is 84°. So,\r\n" );
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document.write( "x is to sin(41°) as 20 is to sin(84°) or\r\n" );
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document.write( "Cross multiplying:\r\n" );
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document.write( "Solve for x by dividing both sides by \r\n" );
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document.write( "Get your calculator:\r\n" );
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document.write( "So the answer nearest that is 13 miles.\r\n" );
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document.write( "Edwin

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