The bisector AD is drawn in the equilateral triangle ABC. The distance from point D to line AC is 6cm. Find the distance from vertex A to line BC.
Since, by condition, triangle ABC is equilateral, its internal angles are 60.
The distance from point D to the AC side is the perpendicular DH, then the triangles DH and DAN are rectangular.
The desired distance AD is the height, median and bisector of the triangle ABC, then the angle DAC = BAC / 2 = 60/2 = 30.
The leg DH of a right triangle lies opposite angle 30, then the length of the hypotenuse AD = DH * 2 = 6 * 2 = 12 cm.
Answer: From point A to side BC 12 cm.
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