The bisector BL of the angle B in the triangle ABC divides the AC side in the ratio 1: 2 (AL: LC = 1: 2)

The bisector BL of the angle B in the triangle ABC divides the AC side in the ratio 1: 2 (AL: LC = 1: 2) What angle does this bisector form with the median drawn from the vertex A?

Let the length of the segment AL = X cm, then CL = 2 * X cm.

By the property of the bisector of the angle of a triangle, it divides the opposite side of the triangle into segments proportional to the adjacent sides.

Then AL / AB = CL / CB.

X / AB = 2 * X / CB.

CB = 2 * AB.

AB = CB / 2.

Since AM is the median of the triangle, then BM = CM = CB / 2.

Then AB = BM = SV / 2, and therefore the triangle ABM is isosceles.

BL is the bisector of the angle ABC, and therefore the bisector of the isosceles triangle ABM, and therefore also its height and median.

Then the angle AOB = 90.

Answer: The angle between the height and the median is 90.