document.write( "Question 84103: Working on a puzzle.
\n" ); document.write( "Assume an equilateral triangle. I'm given 2 points:
\n" ); document.write( "Point A: -13, -116
\n" ); document.write( "Point B: 7, -75\r
\n" ); document.write( "\n" ); document.write( "How do I determine the 3rd point?
\n" ); document.write( "Thanks \n" ); document.write( "
Algebra.Com's Answer #60576 by venugopalramana(3286)\"\" \"About 
You can put this solution on YOUR website!
OK AS DESIRED I AM GIVING THE FULL SOLUTION.
\n" ); document.write( "BUT WHOEVER GAVE THIS PROBLEM APPEARS TO BE MORE KEEN ON GETTING LABORIOUS WORK DONE WITH HORRID NUMBERS THAN CHECKING THE INTELLIGENCE IN METHOD OF APPLICATION
\n" ); document.write( "Working on a puzzle.
\n" ); document.write( "Assume an equilateral triangle. I'm given 2 points:
\n" ); document.write( "Point A: -13, -116
\n" ); document.write( "Point B: 7, -75
\n" ); document.write( "LET C BE (H,K)
\n" ); document.write( "SLOPE OF AC=(K+116)/(H+13)=M SAY
\n" ); document.write( "LET D BE MID POINT OF AB. D IS (7-13)/2,(-75-116)/2=(-3,-95.5)
\n" ); document.write( "SLOPE OF CD =-1/SLOPE 0F AB
\n" ); document.write( "SLOPE OF AB = (-75+116)/(7+13)=41/20
\n" ); document.write( "SLOPE OF CD =-1*(7+13)/(-75+116)=-20/41=(K+95.5)/(H+3)
\n" ); document.write( "-20H/41 -K = 95.5+60/41
\n" ); document.write( "-0.4878H-K= 96.96341463 ……………………………………….1
\n" ); document.write( "TAN(ANGLE CAB)=[M-(41/20)]/[1+41M/20]=TAN(60)=SQRT(3)
\n" ); document.write( "M[1-41{SQRT(3)/20}]=SQRT(3)+(41/20)
\n" ); document.write( "M= -1.482747734 =(K+116)/(H+13)
\n" ); document.write( "-1.48275H-K=116+13*1.48275= 135.27575 ………………………..2
\n" ); document.write( "EQN.1-EQN.2 GIVES
\n" ); document.write( "0.99495 H = -38.31233537
\n" ); document.write( "H = -38.50679468
\n" ); document.write( "PUTTING IN EQN.1
\n" ); document.write( "K= -78.17980019
\n" ); document.write( "HENCE C IS (-38.5068,-78.1798)
\n" ); document.write( "NOW THERE WILL BE ANOTHER C' SATISFYING THE ABOVE REQUIREMENT
\n" ); document.write( "YOU CAN GET C' BY TAKING TAN (ANGLE CAB)=-SQRT(3) IN TO GET EQN.2
\n" ); document.write( "CHECK THE RESULT
\n" ); document.write( "AB^2= 2081 AB= 45.61797891
\n" ); document.write( "BC^2= 2080.979974 BC= 45.61775942
\n" ); document.write( "CA^2= 2080.964374 CA= 45.61758843\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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