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geometry

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in an equilateral triangle RST, R has coordinates (0.0)and T has coordinate of (2a,0).Find the coordinates of S in terms of a.

  • geometry -

    By symmetry, S must lie on the vertical line x=a.
    Let the coordinates of S be (a,y).
    Since the length of one side of the triangle is (2a-0)=2a, we can calculate the distance of (a,y) to (0,0) and equate to 2a accordingly.

    Using Pythagoras theorem,
    (2a)=sqrt(a²+y²)
    Solving for y:
    y²=(2a)²-a²=3a²
    y=(√3)a

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