February 23rd, 2018, 06:21 AM  #1 
Newbie Joined: Feb 2018 From: Iran Posts: 29 Thanks: 3  Equilateral triangle
A vertex of an equilateral triangle is A(2,3) and the equation of opposite side is x+y+2=0. Find the equations of the other two sides. Please explain step by step.
Last edited by skipjack; February 23rd, 2018 at 09:13 AM. 
February 23rd, 2018, 09:33 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,269 Thanks: 1958 
As the given side has slope tan(135°) = 1, the other sides have slopes tan(75°) = 2 + √3 and tan(15°) = 2  √3, and so their equations are y = (2 ± √3)(x  2) + 3. The single equation x²  4xy + y² + 8x + 2y  11 = 0 suffices, as it can be factorized (or solved by using the quadratic formula) to give the above two equations. 

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equilateral, equiletral, triangle 
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