# The bisector AD is drawn in the equilateral triangle ABC.

October 9, 2021 | education

| **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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.