anonymous one year ago Annie walks 15 feet away from her house and places a mirror on the ground. she backs up 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 annies eyes, the mirror and the ground are congruent. what is the length of this house, explain your reasoning.

1. anonymous

2. triciaal

hint similar figures and pythagorean theorem

3. anonymous

I know that but im still confused

4. anonymous

5. anonymous

@dan815

6. triciaal

|dw:1438231729884:dw|

7. triciaal

|dw:1438231818539:dw|

8. anonymous

would it be 11?

9. anonymous

@triciaal

10. triciaal

no solving for h try again

11. anonymous

does it have to do with annie and the house being perpendicular to the ground?

12. triciaal

|dw:1438232282626:dw|

13. triciaal

yes because perpendicular then forms right triangle 2 angles same so you can use ratios

14. anonymous

The triangles are similar because they all have the same angles. The two triangles are both 90˚ angles and they both have another angle that is the same (as indicated by the circle fragment on the picture). That means that the last angle will be the same. Triangles are similar when they have the same angles but don't have to have the same lengths. If the triangles are similar, the side lengths are in ratios. You are given the length of the side that corresponds with the third angle, which are 4 and 15. So the ratio of the lengths of the small to large triangle is 4:15. You are given another length (Height of Annie's eyes), which is 5. This can help you find the height of the house. Let x=height of the house. So 4/15 = 5/x 4x=5*15=75 x=75/4 x=18.75 ft Hopes this helps man :)

15. triciaal

this will give the same result |dw:1438232558848:dw|

16. triciaal

@Icedragon50 agree with your explanation except not 15 use 11 see sketch

17. anonymous

hmm why would we use 11

18. triciaal

look at the original in addition to that 15 - 4 = 11

19. anonymous

Using your method we would still get the same answer tho so both r correct :3 Heres a medal for ya

20. triciaal

we have the same method read above your explanation is correct you cannot get the same answer with different numbers will give you one too

21. anonymous

what was h ?