## anonymous one year ago If the circle with center O has area 9 pi, what is the area of equilateral triangle ABC?

1. anonymous

|dw:1441314908068:dw|

2. misty1212

HI!!

3. anonymous

hey misty!

4. misty1212

area is $$9\pi$$r right?

5. anonymous

yea so the diameter is 6

6. misty1212

ok so you got that the height is 6

7. anonymous

|dw:1441315064479:dw|

8. anonymous

^is that for the height of the triangle? Like we're converting the 6 to an apropriate side that corresponds to the 30-60-90 triangle right?

9. misty1212

you are way ahead of me

10. anonymous

|dw:1441315150836:dw|

11. misty1212

yeah each side of your triangle is $\frac{2\times 6}{\sqrt3}$

12. misty1212

you lost me there height of the triangle is 6

13. misty1212

|dw:1441315234092:dw|

14. misty1212

the short leg of either right triangle on the left and right is $$\frac{6}{\sqrt{3}}$$

15. misty1212

area of each right triangle is base times height

16. misty1212

rather one half base times height but together it is base times height so $6\times \frac{6}{\sqrt3}$

17. misty1212

|dw:1441315367905:dw|

18. anonymous

wait what? so $4\sqrt{3}$ is for the bottom left and right of the traingles?

19. anonymous

how why?

20. misty1212

|dw:1441315446382:dw|

21. misty1212

the short leg is the long leg divided by root 3

22. misty1212

so the area of the two right triangles taken together is base times height

23. misty1212

ok i see $\frac{6}{\sqrt{3}}=2\sqrt3$

24. misty1212

so total area is $6\times 2\sqrt3 = 12\sqrt 3$

25. anonymous

fml i've been doin it all wrong this whole time

26. misty1212

you got the height right away then i think you confused yourself and turned the height in to something else first you said it was 6 (correct) then you said it was $$4\sqrt3$$

27. anonymous

So |dw:1441315715658:dw|

28. misty1212

yeah that looks good to me

29. anonymous

i dont get why it's 2 root 3 is the problem like why does it convert that way and the process

30. anonymous

i thought in a 30-60-90 triangle the root three would replace the 6

31. misty1212

k lets go slow you said you had a 30 - 60 -90 triangle right?

32. anonymous

yea

33. misty1212

the ratios are $1:\sqrt3:2$ for short leg ; long leg ; hypotenuse

34. anonymous

yea

35. misty1212

the long leg here is 6

36. misty1212

so the short leg is $\frac{6}{\sqrt3}=2\sqrt3$

37. anonymous

how?

38. misty1212

you multiply the short leg by root 3 to get the long leg right?

39. misty1212

so to go the other way, from the long leg to the short leg, you divide

40. anonymous

yea but like why is it that way? shouldn't the short leg not contain the root 3?

41. misty1212

lol no it does here

42. anonymous

that so weird

43. misty1212

if the short leg was a whole number the long leg would contain root 3

44. misty1212

but the long leg is a whole number, so the short leg as the root 3 in it

45. misty1212

it is not weird, only seems weird because you usually see it with the short leg a whole number

46. anonymous

hmmmm yea i guess so