A ship has steamed 120 nautical miles North and 230 nautical miles West.
Find the distance
Find her True Course.
To find the distance traveled by the ship, we can use the Pythagorean theorem. If we consider the ship's movement North as the vertical leg of a right triangle and the ship's movement West as the horizontal leg, the distance traveled is equal to the hypotenuse of the triangle.
Using the Pythagorean theorem:
Distance^2 = (North distance)^2 + (West distance)^2
Distance^2 = 120^2 + 230^2
Distance^2 = 14400 + 52900
Distance^2 = 67300
Distance ≈ √67300
Distance ≈ 259.61 nautical miles (rounded to two decimal places)
To find the True Course of the ship, we can use trigonometry. The True Course is the angle between the ship's path and the North direction.
Using inverse tangent (arctan) function:
True Course = arctan(North distance/West distance)
True Course = arctan(120/230)
True Course ≈ 27.54 degrees (rounded to two decimal places)
Therefore, the distance traveled by the ship is approximately 259.61 nautical miles and the True Course is approximately 27.54 degrees.
To find the distance the ship has traveled, we can use the Pythagorean theorem since the ship has traveled both north and west.
Using the Pythagorean theorem, we can calculate the distance as follows:
Distance = √(120^2 + 230^2)
= √(14400 + 52900)
= √(67300)
≈ 259.50 nautical miles
Therefore, the ship has traveled approximately 259.50 nautical miles.
To find the ship's True Course, we can use trigonometry.
True Course = atan(230/120)
≈ 63.43 degrees
Therefore, the ship's True Course is approximately 63.43 degrees.