Posted by **katie** on Sunday, July 3, 2011 at 8:39pm.

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 -
**MathMate**, Monday, July 4, 2011 at 4:31pm
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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