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

znappydooz · Answer

Part 1: Prove the triangles are similar.
Part 2: Determine the height of the house.

znappydooz · Answer

attachment

znappydooz · Answer

@AnswerMyQuestions, can you help?

anonymous · Answer

:O

I did this before

anonymous · Answer

Hold on a minute

anonymous · Answer

We can set up a proportion:

$\dfrac{5}{4} = \dfrac{x}{15}$

Cross multiply and solve for 'x'

anonymous · Answer

5 x 15
5 x $x$

znappydooz · Answer

Wait a moment...
We multiply 5 * 15, but why 5 * x?
Wouldn't it be 4 * x

anonymous · Answer

Yes, it would @AnswerMyQuestions is wrong.

znappydooz · Answer

Alright, so the answer would be...

anonymous · Answer

Oops. LOL

znappydooz · Answer

x = 75/4

anonymous · Answer

Yep, now divide that.

znappydooz · Answer

18 3/4

anonymous · Answer

Yep, so the height of the house is 18 3/4 or18.75 feet.

znappydooz · Answer

Would that be the answer I have to put @iGreen.?

anonymous · Answer

Yes, the height of the house is 18.75. And show your work

znappydooz · Answer

So, we got the angle, but what would be the height of the house?

znappydooz · Answer

@iGreen.

anonymous · Answer

Actually that's the height of the house..

znappydooz · Answer

So that the height of the house?

znappydooz · Answer

Alright, what about the angles?

anonymous · Answer

What about them..? It doesn't tell us to find them.

znappydooz · Answer

Oh sorry, thats not what I meant XD 
I meant to say, how do I find if the triangles are similar? @iGreen.

anonymous · Answer

Well it tells us that the angles are congruent, and we found out that the sides are all proportional so yeah..that pretty much proves it.

znappydooz · Answer

Since it's asking "Prove the triangles are similar." do you think I have to add something?

anonymous · Answer

Yes, of course, just say that the sides are proportional and it tells us some of the angles are congruent.

znappydooz · Answer

This is what I got...

znappydooz · Answer

Part 1:
Since the sides are proportional and it says that some of the angles are congruent, it lets me know that the triangles are similar.
Part 2:
5/4 = x/15
x = 75/4
75/4 = 18 3/4 = 18.75
The height of the house above is 18.75.