## max1409 one year ago 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. Annie and the house are both perpendicular to 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 below: Image depicts a mirror on the ground between a person and a house. The mirror is 4 feet away from the person and 15 feet away from the house. What is the height of the house? S

1. max1409

2. max1409

anyone have any idea?

3. abb0t

anyone have any idea?

4. max1409

@abb0t dude this is a not a chat please stop

5. abb0t

@abb0t dude this is not a chat please stop

6. max1409

@abb0t reported

7. max1409

?

8. anonymous

|dw:1440807663975:dw|

9. max1409

so 4x=75

10. max1409

so x=75/4

11. anonymous

correct

12. max1409

x=18.75

13. max1409

correct/

14. max1409

?

15. anonymous

yes

16. max1409

So i would write side A is 5 side B is 14 D 15 and E is x

17. max1409

@surjithayer

18. max1409

?

19. anonymous

|dw:1440808213300:dw|

20. max1409

so how would i put it in a sentence ?

21. max1409

?

22. anonymous

let AC ( the height of man's eye)=5 ft, B be the position of mirror BE( the distance of mirror from house)=15ft Let height of house DE=x CB (the distance of man from mirror)+4 ft angle of incidence=angle of reflection.

23. max1409

ok

24. anonymous

CB=4 ft

25. max1409

AC is 5 ft B is the position of the mirror Be is 15 ft DE is x CB is 4 ft. So 5 over 4 equals x over 15. So 4x=75 and 75 divided by 4 equals x=18.75

26. max1409

@surjithayer is that good

27. max1409

?

28. anonymous

In triangles ACB and DBE <ABC=<DBE (angle of incidence=angle of reflection) <ACB=<DEB (each right angle) so triangles are similar. Hence sides are proportional. $\frac{ 5 }{ 4 }=\frac{ x }{ 15 },x=?$

29. abb0t

@abb0t reported