## Mimi_x3 4 years ago Amy is 20m S30°W from a tree. Belinda is 50m 110° T from the same tree. Find the distance between them, to the nearest metre.

1. anonymous

what do S30°W and 110° T mean ?

2. Mimi_x3

Um, I'm not sure but i think South 30 degrees West , 110 degrees true bearing idk. I haven't done it in ages so I forgot xD

3. anonymous

|dw:1315630919336:dw|

4. anonymous

like that ^^^ ?

5. anonymous

|dw:1315631114054:dw|

6. Mimi_x3

Um, idk , it looks right though xDD

7. Mimi_x3

How can I find the distance between them ?

8. anonymous

|dw:1315631564224:dw|

9. Mimi_x3

Um, I don't think that it requires sin and cos, its bearings

10. anonymous

|dw:1315631903573:dw|

11. Mimi_x3

What? There's not values of x and y, how can you use the distance formula ?

12. anonymous

I got the values of x and y using the sin() and cos() in the table I drew above. Rounded to the nearest metre, I get 64 meters distance.

13. Mimi_x3

Okay, tyvm (:

14. anonymous

does it make sense ? did you learn this stuff in the past ?

15. Mimi_x3

Not in the past xD, I learnt it year 7 and now I forgot xD But I remember that there's an easier way that doesn't require sin and cos

16. anonymous

Well , if there is an easier way, I hope someone will post it here - coz I'd like to know it too :)

17. Mimi_x3

Hey, you know your diagram what is the angle degrees thing for AB

18. anonymous

what do you mean ?

19. Mimi_x3

|dw:1315632702671:dw|

20. anonymous

yes we can calculate that - it's 240-110 = 130 degrees

21. anonymous

and you're right that we can make the problem simpler

22. Mimi_x3

Yep, there's a formula to calculate it then, was it the sine or cosine formula ? or was it soh cah toa ?

23. anonymous

|dw:1315633004738:dw|

24. Mimi_x3

|dw:1315634036159:dw|

25. anonymous

I would need to calculate to find out - why are you asking ?

26. Mimi_x3

If that angle can be found, then I can use the sine rule xD

27. anonymous

are you trying to use the law of the cosines ?

28. Mimi_x3

No, the Sine Rule it says it in my book xD

29. anonymous

which sine rule ? a/sin(A)=b/sin(B)=c/sin(C) ?

30. anonymous

Yes, that's it @fiddle

31. Mimi_x3

Yep that xD

32. anonymous

yes, but we only have one angle , that 130 degrees at this point.

33. Mimi_x3

I know , but the other angle is 30 right ? the one that I drew

34. anonymous

why did you pick 30 degrees ?

35. anonymous

is it becasue sin(30)=1/2 ?

36. Mimi_x3

Well, the question S30°W so that angle is 30 right ?

37. anonymous

|dw:1315634688115:dw|

38. anonymous

No, you can't say that...@mimi|dw:1315634688202:dw|

39. anonymous

The 30 degrees would be relative to the black line I drew.

40. anonymous

yeah, upsilon says the same thing.

41. Mimi_x3

Can it be 60 then, since 90-30 = 60 ?

42. anonymous

You can't decide like that you need the angle to be in ratio with the opposite sides...

43. anonymous

yep

44. anonymous

but the law of the cosines might work here.

45. anonymous
46. anonymous

Yea, that will work

47. anonymous

|dw:1315635067683:dw|

48. anonymous

$d = \sqrt{ a^2 + b^2 - 2*a*b*cos\alpha}$

49. Mimi_x3

Okay, tyvm (:

50. anonymous

http://www.wolframalpha.com/input/?i=sqrt%2820^2%2B50^2-2*20*50*cos%28130%29%29 It's 64 , same answer I got with the first method :)

51. Mimi_x3

Ok, ty (:

52. anonymous

and it's much shorter than the first method :)

53. Mimi_x3

yup xD. Your method looked so complicated before (: