A person walks 44° north of east for 3.64 km. How far would another person walk due north and due east to arrive at the same location?

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## Answers (2)

Sit down and draw cross and label them with the cardinal ponts: N, S, E and West . North at the top, South at the bottom and West on the left and East on the right (easy to remember if you read as "we" left to right) .

From the point where the lines intersect (we shall call it 'O' point), draw a line sloping upwards to the right pointing towards approx 2 o'clock position, it does not really matter about exact position. The length of the this sloping line label as 3.64 km. Now label the angle between this line and the Line marking East as 44 Degrees. At the point where the line ends (and make it a decent length draw a horizontal line to reach the North line you have drawn. also, from the point where the sloping line ends draw a line downwards to meet the East line.

The length or the North line from the 'O' point is given by 3.64 sin (44)

The length or the East line from the 'O' point is given by 3.64 cos (44)

3.64 sin (44) =3.64 x 0.6946 = 2.53 km

and

3.64 cos(44) = 3.64 x 0.719 = 2.62 km

So,

The person will have to walk 2.53km due north from the eastern line to reach the same point and

The person will have to walk 2.62 km due east on the north line to reach the same point

North component of 3.64km. walk = (sin 44) x 3.64 metres, = 2.52856, or 2.53km. using 2 decimal places.

East component = (cos 44) x 3.64, = 2.62km.

That's the north and east magnitudes the other person would need to walk.