The
horizontal component of an angular distance can be calculated by multiplying the
distance with the cosine of the angle, Dx = D * cos θ
While
the vertical component is calculated by multiplying the distance with the sine
of the angle, Dy = D * sin θ
The
resultant displacement can then be obtained using the formula for hypotenuse
and summations of each component:
R^2
= (summation of Dx)^2 + (summation of Dy)^2
summation
of Dx = 600 * cos47 + 500 * cos128 + 300 * cos209 + 400 *
cos(-77) = -71.0372
summation of Dy = 600 * sin47
+ 500 * sin128 + 300 * sin209 + 400 * sin(-77) = 297.6267
<span> Note: you have to draw the lines to correctly
determine the angles</span>
R^2 = (-71.0372)^2 + 297.6267^2
R = 306 m
The resultant angle is:
tan θ = Dy / Dx
θ =
tan^-1 (297.6267 / -71.0372)
θ =
103˚ = [N 13˚ W]
Therefore
displacement is 306 m <span>[N 13˚ W].</span>
