## anonymous one year ago A ship leaves port A and travels for 60km in the direction 38 degrees. it then sails 40km in the direction 128 degrees to an island B . a) how far is B from A ? b)if the ship wishes to sail back directly to A from B , in what direction must it sail ?

1. welshfella

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2. welshfella

you need to find the length of AB

3. welshfella

to do this we need to find the value of angle ACB then we use the Cosine Rule to fin AB

4. welshfella

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5. welshfella

angle ACB = 38+52 = 90 degrees so triangle ACB is right angled so we dont need the cosine rule Just use the pythagoras theorem AB^2 = 60^2 + 40^2

6. welshfella

can you find AB?

7. welshfella

just add 40^2 + 60^2 then take the square root

8. welshfella

9. anonymous

I GET 10

10. welshfella

??? 60^2 = 3600 40^2 = 1600 adding 5200 so AB^ 2 = 5200 AB = sqrt 5200

11. welshfella

use your calculator to find the square root of 5200

12. anonymous

72.11

13. welshfella

yes so distance from A to B is 72 km

14. welshfella

* sorry 72.11

15. anonymous

and b) the direction ?

16. welshfella

b) the directions always start from the North line and are clockwise

17. welshfella

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18. welshfella

Its the angle I've drawn around the point B

19. anonymous

so its 270 ?

20. welshfella

No its not 270 we need to find the value of angle CBA the angle next to it is 52 degrees then our direction will be 360 - 52 - <CBA

21. anonymous

this is confusing

22. welshfella

as triangle ABC is right-angled we casn use trigonometry tan CBA = 60/40 = 1.5

23. welshfella

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24. welshfella

does that make it clearer?

25. welshfella

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26. welshfella

that angle is 52 degrees as they are interior alternate angles

27. welshfella

tan CBA = 1.5 so you can find angle CBA

28. welshfella

then the direction = 360 - 52 - <CBA

29. anonymous

306.5

30. welshfella

what did you get for angle CBA?

31. anonymous

308 degrees

32. welshfella

??? noo on your calculator enter tan-1 then 1.5 - or on some its the other way around

33. anonymous

56.31

34. anonymous

whats 108 for ?

35. welshfella

360 - 52 - 56.3

36. welshfella

forget the 108 - i got confused also!!

37. anonymous

yea

38. anonymous

nd whats 56.3 for ?

39. welshfella

thats the value of angle CBA

40. anonymous

BUH YEW SAID 360-52= ANGLE CBA WHICH IS 308

41. welshfella

so now you have what you require to find the direction it is 360 - 52 -56.3

42. welshfella

no i didnt say that

43. anonymous

OK NVM

44. welshfella

so what do you get for the direction?

45. anonymous

251.7

46. welshfella

yep thats it

47. anonymous

duh thanks

48. welshfella

yw

49. anonymous

|dw:1432992810256:dw| im send in the question .. pleas ehelp me with this last question

50. anonymous

a coast guard sees a boat B on the bearing of 30 degrees and a yatch Y on a bearing of 72 degrees . the bearing of the yatch from a boat is 136 degrees. a) calculate the values of D , E, F , the three angles of triangle CBY. b) what is the bearing of the coast guard from the yatch ?