The equation of one side of an equilateral triangle is `x-y=0\ ` and one vertex is `(2+sqrt(3),\ 5)` . Prove that a second side is `y+(2-sqrt(3))x=6` and find the equation of the third side.

Explanation

Let the given vertex be` A(2+sqrt(3)
​,5)` of the equilateral triangle ABC and


x−y=0 be the equation of line BC.


We have to find the equations of sides AB and AC, each of which makes an angle of` 60^o` with line x−y=0

We know that the equation of two lines passing through a point (x,y) and making an angle θ with the line whose slope is m is,

`y−y_1​=(m±tantheta)/(1∓tantheta)​(x−x_1​)`

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