Please help I give you hugs and cookies forever

Question

Please help I give you hugs and cookies forever <3 best answer gets a medal :3 pwease?

Peter walks 30 feet away from his house and places a mirror on the ground. He backs 6 feet away from the mirror so that he can see the tip of the roof. Peter's eyes are 5 feet above the ground. The angles between the top of the house, the mirror, and the ground and between Peter's eyes, the mirror, and the ground are congruent as shown in the image:



Part 1: Prove the triangles are similar.
Part 2: Determine the height of the house.

fallonbanks · Answer

attachment

gamer56 · Answer

im not sure im sorry

fallonbanks · Answer

its otay -_-

fallonbanks · Answer

@mathman806 Help? @mathmale @Cutie1234

mathmale · Answer

FB:  Why not copy down that illustration onto paper or into a Draw screen, and then label everything you can?  

It will be helpful indeed to see that the smaller triangle has height 5 fet and width 6 ft.
The distance from the mirror to the house is 30 ft; mark that too.  Repr. the height of the house by y. 

It's been years since I last looked into a geometry textbook, but instinctly I "know" the two triangles are similar because they share a common angle.

If they are similar, then ratios of their sides are equal:
$$\frac{ 5 }{ 6 }=\frac{ y }{ 30 }.$$
Solve for the height of the house, y.

fallonbanks · Answer

:O ^-^ you just made my day!!!!! thankies soooooo much ^-^ *gives you cookies and a medal* I hope you have an awesome day :3

mathmale · Answer

No hug?  :)   Perhaps you could send me an e-hug (whatever that is).  Very happy to help.  Thanks.

fallonbanks · Answer

*hugs you super tight* :3 there ya go

mathmale · Answer

thanks so much.  Now it's YOU who made MY day.  :)

fallonbanks · Answer

wait o-o im still confused on how I do the math x-x im stupid @mathmale

mathmale · Answer

Cross multiply that equation:$$\frac{ 5 }{ 6 }=\frac{ y }{ 30 }\rightarrow 150+6y$$
Then solve for y.  :)

fallonbanks · Answer

oh okay, so would this also prove the triangles are similar?

mathmale · Answer

No.  Afraid I'm going to have to ask you to look that kind of proof up in your textbook or workbook, if you have one, or to do an Internet search for "similar triangles," or to post the proof of the fact that the triangles are similar as a new question on OpenStudy.  Don't remember.  Hugs to you too.

fallonbanks · Answer

aw okay, well thanks for all the help ^-^

mathmale · Answer

You're very welcome!  MM