In an isosceles triangle ABC with an AC base of 12 inches and an angle B of 120 degrees.

In an isosceles triangle ABC with an AC base of 12 inches and an angle B of 120 degrees. Find the distance from point A to point BC.

Since the angle ABC is obtuse, the distance from point A to straight line BC is the height AH drawn for the continuation of BC,

The angle ABH is adjacent to the angle ABC, the sum of which is 180, then the angle ABH = (180 – ABC) = (180 – 120) = 60.

In a right-angled triangle ABH, the angle BAH = (90 – ABH) = (90 – 60) = 30.

The BH leg lies opposite the angle 30, then its length is equal to half the length of the hypotenuse AB.

BH = AB / 2 = 12/2 = 6 cm.

Answer: From point A to side BC 6 cm.