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 ?

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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 ?

Mathematics
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|dw:1432990003731:dw|
you need to find the length of AB
to do this we need to find the value of angle ACB then we use the Cosine Rule to fin AB

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|dw:1432990207184:dw|
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
can you find AB?
just add 40^2 + 60^2 then take the square root
use your calculator
I GET 10
??? 60^2 = 3600 40^2 = 1600 adding 5200 so AB^ 2 = 5200 AB = sqrt 5200
use your calculator to find the square root of 5200
72.11
yes so distance from A to B is 72 km
* sorry 72.11
and b) the direction ?
b) the directions always start from the North line and are clockwise
|dw:1432991016454:dw|
Its the angle I've drawn around the point B
so its 270 ?
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 -
this is confusing
as triangle ABC is right-angled we casn use trigonometry tan CBA = 60/40 = 1.5
|dw:1432991546898:dw|
does that make it clearer?
|dw:1432991638985:dw|
that angle is 52 degrees as they are interior alternate angles
tan CBA = 1.5 so you can find angle CBA
then the direction = 360 - 52 -
306.5
what did you get for angle CBA?
308 degrees
??? noo on your calculator enter tan-1 then 1.5 - or on some its the other way around
56.31
whats 108 for ?
360 - 52 - 56.3
forget the 108 - i got confused also!!
yea
nd whats 56.3 for ?
thats the value of angle CBA
BUH YEW SAID 360-52= ANGLE CBA WHICH IS 308
so now you have what you require to find the direction it is 360 - 52 -56.3
no i didnt say that
OK NVM
so what do you get for the direction?
251.7
yep thats it
duh thanks
yw
|dw:1432992810256:dw| im send in the question .. pleas ehelp me with this last question
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 ?

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