A ladder is placed so that its foot is 2 m from a wall. The ladder touches the top of a 2 m fence that is 1.5 m from the wall. State how you know the two triangles in the diagram are similar. How high up the wall does the ladder reach?

Answer 1

well, I do not see your diagram but suspect you mean the two triangles under the latter which share the angle at the ladder/ground point and a right angle at the base of the fence and the wall. Therefore angle-angle -angle ---> similar

.5/2 = 2/h
h = 4/.5 = 8 meters high

Answer 2

Thank you so much for your answer, Damon, i'm new to trigonometry and i'd like to know why it's necessary to do 2 - 1.5 to get 0.5? Thanks! much appreciated.