Question 1011928: Please help me solve this question
If 'a' is the length of one of the sides of an equilateral triangle ABC, base BC lies on X - axis and vertices B is at the origin, find the coordinates of the vertices of triangle ABC
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! The two obvious vertices are at (0,0) for A, and (0,a) for B.
Point C is at a distance from the x-axis and this distance will be the altitude size from point C to the point ( a/2, 0 ). This altitude cuts the triangle into two special 30-60-90 triangles.
Either of these special triangles has hypotenuse a, leg a/2, and you can find the size of the other leg, the altitude of the equilateral triangle. Call this size, y.
Solve for y.
You will want the PLUS square root form.
Your point C will be, whatever you find for y, C (a/2, y).
Answer by MathTherapy(10556)  (Show Source):
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