Annie walks 15 feet away from her house and places a mirror on the ground. She backs 4 feet away from the mirror so that she can see the tip of the roof. Annie's eyes are 5 feet above the ground. The angles between the top of the house, the mirror, and the ground and between Annie's eyes, the mirror, and the ground are congruent as shown in the image:

Question

anonymous · Answer

Here's the picture. Thanks!

anonymous · Answer

The triangles are similar by the reason AA similarity (angle-angle) and because they are similar the sides are in proportion. 4/5 =15/x then cross multiply:
4x = 75
x=75/4
x=18.75 feet

anonymous · Answer

But how do you get the second angle for the AA postulate? The only given ones are the marked ones.  Do you have to assume that they're right triangles? @texaswins

phi · Answer

They probably want you to know that the standing person forms a 90º angle with the ground...same for the wall of the house.

anonymous · Answer

Alright thanks, that's what I wanted to know.  I don't know how else it would work out so I'll just go ahead and assume they're right angles.