document.write( "Question 1148503: ABC is a right angle isosceles triangle, angle BCA = 90, with BC as the base and AB as hypotenuse side AC = BC. Point M is at midpoint on hypotenuse such that BM=MA=36cm. P and Q are points on sides BC and AC respectively. An equilateral triangle is formed by joining MPQ. Find the area of equilateral triangle MPQ. \n" ); document.write( "

Algebra.Com's Answer #769875 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "1.  Make a sketch.\r\n" );
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document.write( "2.  Due to symmetry,  angle BMP = angle AMQ = 60°.\r\n" );
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document.write( "3.  Consider triangle BMP.\r\n" );
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document.write( "    Its side BM is 36 cm;  its side MP is unknown; let it be \"a\" cm long.\r\n" );
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document.write( "    Its angle BMP is 60°; its angle MBP is 45°.\r\n" );
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document.write( "    Its angle MPB = 180° - 60° - 45° = 105°.\r\n" );
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document.write( "4.  Apply the sine law theorem to triangle BMP.\r\n" );
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document.write( "         = .    (1)\r\n" );
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document.write( "    Use  sin(105°) = sin(180°-105°) = sin(75°) = sin(45°+30°) = sin(45°)*cos*30°) + cos(45°)*sin(30°) =  = .\r\n" );
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document.write( "    Use  sin(45°) = .\r\n" );
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document.write( "    Then from (1)  you get\r\n" );
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document.write( "        a =  =  = .   (2)\r\n" );
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document.write( "    It is the final formula for the unknown side length \"a\".\r\n" );
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document.write( "    If in addition to the final formula (2) you need its numerical value,\r\n" );
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document.write( "    here it is   a = 26.354 centimeters,  with 3 correct decimal places after the decimal dot.\r\n" );
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document.write( "     Now, if you want to find the area of the triangle MPQ, use the formula\r\n" );
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document.write( "        area =  =  = 300.74 cm^2.\r\n" );
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