Paul walks 25 feet away from his house and places a mirror on the ground. He backs 5 feet away from the mirror so that he can see the tip of the roof. Paul's eyes are 6 feet above the ground. Paul and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Paul's eyes, the mirror, and the ground are congruent as shown in the image below:

What is the height of the house? Show your work and explain your reasoning in complete sentences.

Question

Paul walks 25 feet away from his house and places a mirror on the ground. He backs 5 feet away from the mirror so that he can see the tip of the roof. Paul's eyes are 6 feet above the ground. Paul and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Paul's eyes, the mirror, and the ground are congruent as shown in the image below:

What is the height of the house? Show your work and explain your reasoning in complete sentences.

anonymous · Answer

I will fan and medal

anonymous · Answer

@ganeshie8

taramgrant0543664 · Answer

The first thing you have to do is determine the angle of the mirror you know that Paul is 5 feet away from the mirror and Paul is 6 feet so you can determine the angle (let's say we will represent this angle as M as it's the angle with the mirror) so the equation is tanM=opposite over adjacent so tanM=6/5

taramgrant0543664 · Answer

Then since we will have the angle and we know that Paul is 25 feet away from the house we can do sort of the same thing as we did above (I will represent the height of the house with the variable H) we can use the same equation as above so we will get:
tanM=H/25

anonymous · Answer

ok

anonymous · Answer

soo what would be the answer im sorry i dont have a calculaor with me

radar · Answer

similar triangles, I am guessing the house is 30 ft to the tip of the house.

taramgrant0543664 · Answer

The house would be 30ft