Answer: option C.
Step-by-step explanation:
If city X is in the point (0,0)
Now, we can use that a displacement of L in distance with an angle A, gives us that the components of the displacement are:
X = L*cos(A)
Y = L*sin(A)
So we know that the city Y is located in:
(40m*cos(40°), 40m*sin(40°))
Now, from this point he moves other 40m with an angle of 140°.
The new position is
(40m*cos(40°) + 40m*cos(140°), 40m*sin(40°) + 40m*sin(140°))
this is:
40m*(cos(40°) + cos(140°), sin(40°) + sin(140°)) = 40m*( 0, 1.28)
the new position is (0, 51.2m)
This means that for a new displacement L and angle A we have:
X = L*cos(A) = 0
Y = L*sin(A) = 51.2m
Cos(A) is only 0 when A = 90° or 270°,
and we know that sin(90°) = 1 and sin(270°) = -1
As we have a positive number in the Y equation, we can conclude that A must be 90°.
Then
Y = L*sin(90°) = L = 51.2m
Here we finded that the bearing of Z from city X is 90°
