Height problem

Question

ABC is an isosceles triangle

BC is 20

AB and AC is 30

Angle A is 120°

Angle B is 30°

Angle C is 30°

 

Please find height of this triangle using both and ONLY pythagorus theorum and Trigonometric values (30:60:90)

 because im getting different heights. really confusing

Answer 1

The measures of the sides do not fit into a 30-60-90 triangle!

By 30-60-90, the height is 15√3

By Pythagoras the height is 40√2