In an isosceles triangle ABC, angle B = 120, AB = 16cm. Find the length of the height BD.

Since triangle ABC is isosceles, the height BD is drawn to its base, then BD is the median and bisector of triangle ABC.

Then the angle ABD = ABC / 2 = 120/2 = 60.

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

Leg BD lies opposite angle 30, then its length is equal to half the length of hypotenuse AB.

BD = AB / 2 = 16/2 = 8 cm.

Answer: Length height BD is 8 cm.