After leaving port, a ship sails 147.0 km in the direction N48o47'E.
How far North of the port is the ship now located? (report your final answer to one decimal place)
Did you draw a diagram? review your basic trig functions? If so, then it should be clear that the answer is
147.0 cos 48°47'
Direction = 48.78 Degrees E. of N.
Disp. = 147km[48.78] = 147*sin48.78 + 147*cos48.78i
Disp. = 110.6 + 96.9i.
d = 96.9 km north of port.
To determine the distance the ship is located North of the port, we need to first understand the given direction.
The direction N48o47'E can be broken down into two components: northern component (N48) and eastern component (47'E).
The northern component, N48, represents 48 degrees North of the reference direction, which is due North.
Given that 1 degree of latitude is approximately equal to 111.32 km, we can calculate the distance North of the port by multiplying 111.32 km by the northern component, which is 48.
Distance North of the port = 111.32 km/degree * 48 degrees = 5337.36 km
Therefore, the ship is located approximately 5337.4 km North of the port.