A ship sailed from a port A on a bearing of N56°E covering a distance of 85km to another Port B. How far is the ship now due north from Port A?
To calculate the distance the ship is now due north from Port A, we need to find the northward component of the distance it traveled.
The northward component can be found using the angle of N56°E, which can be split into a northward direction (N) and an eastward direction (E).
The northward component can be found using the formula:
northward distance = total distance * cosine(angle)
Total distance = 85 km
Angle = N56°E
Splitting the angle into northward and eastward components:
Northward component = N * cosine(angle) = 85 km * cosine(56°)
Using a calculator, the northward component is approximately:
Northward component = 85 km * cosine(56°) = 54.768 km
Therefore, the ship is now approximately 54.768 km due north from Port A.