HELP!!!
Sarah walks 20 feet away from her house and places a mirror on the ground. She backs 5 feet away from the mirror so that she can see the tip of the roof. Sarah's eyes are 4 feet above the ground. Sarah and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Sarah's eyes, the mirror, and the ground are congruent as shown in the image below:

What is the height of the house?

Question

HELP!!!
Sarah walks 20 feet away from her house and places a mirror on the ground. She backs 5 feet away from the mirror so that she can see the tip of the roof. Sarah's eyes are 4 feet above the ground. Sarah and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Sarah's eyes, the mirror, and the ground are congruent as shown in the image below:

What is the height of the house?

anonymous · Answer

attachment

pinklion23 · Answer

HOLY SH*T i will do my best of helping you :)

anonymous · Answer

Thanks! I appreciate it. :-)

pinklion23 · Answer

What do you think the answer is

pinklion23 · Answer

The triangles are similar by AA similarity

anonymous · Answer

I think that to find it, you have to set up the triangles proportionally, so you have 5 over 20  is equal to 4 over x. Then you solve for x. Would that be correct?

pinklion23 · Answer

2 angles of one triangle are congruent to 2 angles of the second triangle.

pinklion23 · Answer

20/5=x/4
so then cross multiply

pinklion23 · Answer

once u cross multiply u get 5x = 80, then solve it to the height

anonymous · Answer

Ok. Thanks! You answered my question. :-D

pinklion23 · Answer

no problem and i the height is 16 feet :)