The side of an equilateral triangle is 12√3. Find the median of this triangle.

1. Vertices of triangle A, B, C. BE – median. AB = BC = AC = 12√3 units.

2. By the condition of the problem, the sides of this triangle are equal. Consequently, its angles are also equal.

The degree measure of each of them is 60 °.

3. Consider triangle ABE. ∠ВЕС= 90 °, since the median in an equilateral triangle also performs the functions of height.

4. We calculate the length of the median BE in terms of one of the trigonometric functions ∠A (sine):

BE / AB = sine ∠A sine 60 ° = √3 / 2.

BE = 12√3 x √3 / 2 = 18 units.