Question

If (0,0), (5,0) and (x,y) are the vertices of an equilateral triangle, find x and y.

Answer 1

let, Point A = (0,0) , B = (5,0) , C = (X,Y)

then, AB = 5 (in x-direction)
also, AB=BC=CA (since triangle is equilateral)
now,
draw a vertical line from point C on line AB and mark as D.
so, Y = CD and AD=DB = AB/2 = 5/2
now, from ∆ BCD,
CD = √(BC^2 - BD^2)
=> Y = √{(5)^2 - (5/2)^2} = (5√3)/2

now,
draw a horizontal line from C on y-axis and mark as point E
so, X = CE also, CE = AD = 5/2
hence,
the value of X = 5/2 and Y = (5√3)/2
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I hope this helps you....