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Given 2 lines L1= 3x+4y+10=0 and L2= 3x+4y+5=0 and an equilateral triangle ABC is constructed such that A(2,0) and BC lies on L1,L2 respectively; find the length of Side of the equilateral triangle Also if ‘theeta’ is the angle between L1 and line AB then tan(theeta) =?

Given 2 lines L1= 3x+4y+10=0 and L2= 3x+4y+5=0 and an equilateral triangle ABC is constructed such that A(2,0) and BC lies on L1,L2 respectively; find the length of Side of the equilateral triangle
Also if ‘theeta’ is the angle between L1 and line AB then tan(theeta) =?

Grade:11

1 Answers

Ajay
209 Points
6 years ago
Point A(2, 0) does not lie on line L2 but still question be solved as follows
Let Point A be any point on line L1 and B and C are points on L2
The distance between L1 and L2 is given by
(10-5)/sqrt(9+16)  = 1
Let D be foot of prependicular from A to BC, then AD = 1 (distance between lines)
Clearly sin60 = AD/AB where AB is side of traingle
AB = AD/sin60 =  2/(sqrt(3))

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