Question 1202456
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Answer: <font color=red>64.6965 km (approximate)</font>



Explanation:


Draw an xy axis.
Place point C at the origin.


The car drives north at 40 kph for 1 hour.
Distance = rate*time
Distance = (40 kph)*(1 hr)
Distance = 40 km
The car drives 40 km north for the first leg of the trip.
Move from point C(0,0) to point A(0,40)


For the next leg of the trip, we have
Distance = rate*time
Distance = (40 kph)*(1/2 hr)
Distance = 20 km
This will move us from A(0,40) to B(20,40) when going 20 km east.


The notation N 30 E means "face north, then turn 30 degrees eastward". 
This is equivalent to the notation E 60 N where we face east and then turn 60 degrees toward the north.
30+60 = 90
See this page for more info about compass bearings.
<a href = "http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/comp.html">http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/comp.html</a>


The notation E 60 N is more useful because 60 degrees is the reference angle. 
Use polar coordinates as an offset to move from B(20,40) to D(30,57.320508)


The scratch work to determine the x,y coordinates of D are shown in this paragraph
r = distance traveled for the remaining 1/2 hr = 20 km
theta = 60 degree reference angle
(xB,yB) = x and y coordinates of point B
x = xB + r*cos(theta)
x = 20 + 20*cos(60)
x = 30
y = yB + r*sin(theta)
y = 40 + 20*sin(60)
y = 57.320508 which is approximate
Make sure your calculator is in degree mode.


To recap the journey:<ul><li>Start at C(0,0)</li><li>Move 40 km north to arrive at A(0,40)</li><li>Move 20 km east to get to B(20,40)</li><li>Move 20 km along the compass bearing N 30 E (aka E 60 N) to arrive at the approximate location D(30,57.320508)</li></ul>The pathway is C to A to B to D in that exact order.


The question is: how far is it from the start point C(0,0) to the end point D(30,57.320508)?


We could draw a right triangle and use the pythagorean theorem.
Or we could use the distance formula.


I'll use the distance formula.
(x1,y1) = (0,0) and (x2,y2) = (30,57.320508)
{{{d = sqrt( (x1-x2)^2 + (y1-y2)^2 )}}}
{{{d = sqrt( (0-30)^2 + (0-57.320508)^2 )}}}
{{{d = sqrt( (-30)^2 + (-57.320508)^2 )}}}
{{{d = sqrt( 900 + 3285.64063737806 )}}}
{{{d = 64.6965272435706}}}
{{{d = 64.6965}}}
This is the approximate distance from C(0,0) to D(30,57.320508)
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