In triangle sides: 20cm, 24cm, 30cm. into which segments will the side of the bisector

In triangle sides: 20cm, 24cm, 30cm. into which segments will the side of the bisector, drawn from a smaller angle, split? indicate the largest of them.

Solution:
Let’s call a triangle ABC, where AB = 20 cm, BC = 30 cm, AC = 24 cm. In a triangle, the smaller angle lies against the smaller side, i.e. the smaller angle is C, and the base of the bisector (K) from the angle C will lie on the side AB: AB = AK + K.
Let us express AK:
AK = AB-KB = 20-BK (cm).
T. about the bisector: the bisector of the angle divides the side of the triangle in a ratio equal to the ratio of the adjacent sides:
(AK / BK) = (AC / BC) = (24/30),
AK = 0.8 * BK,
20-BK = 0.8 * BK,
BK = 11 + 1/9 (cm).
AK = 20- (11 + 1/9) = 8 + 8/9 (cm).