## anonymous one year ago The diagram below shows a pentagram (a five-pointed star) inscribed inside a regular pentagon. There are several golden ratios in this figure This means that if length a = 1, then length b = 1.618. In this case, what is length c?

1. anonymous
2. anonymous

@amoodarya

3. amoodarya

|dw:1436206053970:dw| can you tell me what is alpha angle ?

4. anonymous

its....

5. anonymous

a=1

6. anonymous

wait wait

7. anonymous

A. 1.618 B. 0.618 C. 2.618 D. 3.142 E. 3.718

8. anonymous

anyways

9. anonymous

a=1

10. anonymous

b=1.618

11. amoodarya

|dw:1436206193343:dw|

12. anonymous

we just need to find c

13. amoodarya

$\alpha=\frac{360}{5}*\frac{1}{2}=36$

14. anonymous

ok

15. amoodarya

|dw:1436206278366:dw|

16. anonymous

thats not in the choices

17. amoodarya

now use cosine law $b^2+c^2-a^2=2bccos (A)\\b^2+c^2-b^2=2 bc \cos(36)\\c^2=2bccos(36)\\ \div c\\c=2bcos(36)$

18. anonymous

its d

19. amoodarya

it is in choices try to find c

20. amoodarya

c=2*b*cos(36)

21. amoodarya

it is not d

22. anonymous

wait

23. anonymous

its not b or d

24. amoodarya

(b+d)/2

25. anonymous

its aT_T

26. amoodarya

2*1.618 *.80

27. amoodarya

"c"

28. anonymous

thx