x is the distance straight east
a) The right triangle representing the scenario is shown below
G is the starting point
F is the final point
x is the distance straight east
y is the distance straight North
The required angle = 90 - 30 = 60
Taking 30 degrees as the reference angle,
hypotenuse = 5
adjacent side = x
opposite side = y
To find x, we would apply the cosine trigonometric ratio which is expressed as
cosθ = adjacent side/hypotenuse
Cos 60 = x/5
By cross multiplying,
x = 5cos60 = 2.5
To find y, we would apply the sine trigonometric ratio which is expressed as
cosθ = opposite side/hypotenuse
Sin 60 = y/5
By cross multiplying,
y = 5Sin60 = 4.33
Thus, the distances are
2.5 km east
4.33 km North
b) If the east and north legs are reversed, the route would be GBF
GB(north) = 5cos30 = 4.33 km
BF(east) = 5sin30 = 2.5 km
The distances are the same. Thus, you will still arrive at the same point