eroshea 3 years ago An isosceles triangle ABC, in which AB=BC=6 root 2 and AC=12 is folded along the altitude BD so that planes ABD and BDC form a right dihedral angle. Find the angle between side AB and its new position.

1. experimentX

could you draw a bit of figure?

2. eroshea

i can't .. that is my problem, too..

3. experimentX

|dw:1353425869624:dw|

4. experimentX

|dw:1353426012864:dw|

5. eroshea

so what i'm going to find is the theta??

6. eroshea

Find the angle between side AB and its new position. what does this mean?

7. experimentX

i guess that's the angle you are going to find ... can you find it?

8. eroshea

i need further solution/explanation

9. experimentX

|dw:1353426445410:dw|

10. eroshea

that is 90 degrees

11. eroshea

i used cosine law

12. experimentX

$$\theta$$ will be half of $$\alpha$$

13. eroshea

45 ?

14. eroshea

the book's answer is 60 degrees.. but i find it 45 degrees.. how did it ended up with 60?

15. experimentX

yep .. should be around like that if you did it properly!!

16. eroshea

aawww. can you explain it ?

17. experimentX

looks like you did it right http://www.wolframalpha.com/input/?i=12^2+%3D+2%286+sqrt%282%29%29^2+-+2+*+%286+sqrt%282%29%29^2+cos%28x%29

18. eroshea

b^2 = a^2 + c^2 - 2ac cos theta that is cosine law right? and the answer is 90 degrees