document.write( "Question 468892: ABC is an right angled triangle,right angled at B.Internal bisector of angle B meet AC at D.AB=3cm,BC=4 cm, find AD. \n" ); document.write( "
Algebra.Com's Answer #321700 by Edwin McCravy(20055)\"\" \"About 
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ABC is an right angled triangle,right angled at B.Internal bisector of angle B meet AC at D.AB=3cm,BC=4 cm, find AD.
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document.write( "Looking at the big right triangle ABC, and the\r\n" );
document.write( "fact that the tangent is \"OPPOSITE%2F%28ADJACENT%29\"\r\n" );
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document.write( "\"tan%28%22%3CA%22%29+=+%28BC%29%2F%28AB%29+=+4%2F3\"\r\n" );
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document.write( "Use the inverse tangent on a calculator to find ∠A:\r\n" );
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document.write( "∠A = 53.13010235°\r\n" );
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document.write( "We know that ∠ABD is 45° because BD bisects the right angle at B\r\n" );
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document.write( "We find ∠ADB by using the fact that\r\n" );
document.write( "the sum of the interior angles of ᅀABD is 180°\r\n" );
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document.write( "∠A + ∠ABD + ∠ADB = 180° \r\n" );
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document.write( "∠ADB = 180° - ∠A - ∠ABD\r\n" );
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document.write( "∠ADB = 180° - 53.13010235° - 45° = 81.86989765°\r\n" );
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document.write( "So we use the law of sines:\r\n" );
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document.write( "\"%28AD%29%2Fsin%28%22%3CABD%22%29=%28AB%29%2Fsin%28%22%3CADB%22%29\"\r\n" );
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document.write( "Cross-multiplying:\r\n" );
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document.write( "\"AD%2Asin%28%22%3CADB%22%29=AB%2Asin%28%22%3CABD%22%29\"\r\n" );
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document.write( "Divide both sides by \"sin%28%22%3CADB%22%29\":\r\n" );
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document.write( "\"AD=%28AB%2Asin%28%22%3CABD%22%29%29%2Fsin%28%22%3CADB%22%29\"\r\n" );
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document.write( "\"AD=%283sin%28%2245%B0%22%29%29%2Fsin%28%2281.86989765%B0%22%29\"\r\n" );
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document.write( "Work out the right side with a calculator:\r\n" );
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document.write( "AD = 2.142857143cm\r\n" );
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document.write( "Edwin
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