document.write( "Question 1148023: Find b such that the points A(2,b),B(5,5)and C(-6,0) are the vertices of right angled $\"highlight%28triangle%29\"$ with angle < BAC = 90 degree. \n" ); document.write( "

Algebra.Com's Answer #769415 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by @Boreal is uncompleted.\r
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\n" ); document.write( "\n" ); document.write( "            The solution by @greenestamps is incorrect.\r
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document.write( "The right angle is at A, so segments BA and CA are perpendicular. Hence, their slopes are inversely opposite.\r\n" );
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document.write( "AB slope: \r\n" );
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document.write( "AC slope: \r\n" );
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document.write( "The condition of perpendicularity is THIS equation\r\n" );
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document.write( "     = \r\n" );
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document.write( "saying that the slope AC is inversely opposite to the slope AB.\r\n" );
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document.write( "Simplify and solve for \"b\" :\r\n" );
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document.write( "     = -24\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "Factor the quadratic polynomial in the left side\r\n" );
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document.write( "    (b-8)*(b+3) = 0.\r\n" );
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document.write( "The two roots are  b= 8  and  b= -3.\r\n" );
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document.write( "ANSWER.  The problem has two solutions  b= 8  and  b= -3.\r\n" );
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