In triangle ABC, angle A = 70 degrees, angle C = 75 degrees, AA1 is the bisector

In triangle ABC, angle A = 70 degrees, angle C = 75 degrees, AA1 is the bisector of triangle ABC, segment BA1 = 4cm. Find the length bisectors АА1.

In the triangle ABC, we calculate the value of the angle ABC.

Angle ABC = (180 – BAC – ACB) = (180 – 70 – 75) = 35.

The segment AA1 is the bisector of the angle BAC, then the angle CAA1 = BAA1 = BAC / 2 = 70/2 = 35.

Then in triangle АА1В the angles at the base of AB are equal to 35, and therefore, triangle АА1В is isosceles, АА1 = BA1 = 4 cm.

Answer: The length of the bisector AA1 is 4 cm.