A ship has steamed 120 nautical miles North and 230 nautical miles West.
Find the distance made good.
Find her True Course.
To find the distance made good, we can use the Pythagorean theorem. The ship has traveled 120 nautical miles north and 230 nautical miles west, forming a right triangle. The distance made good is the hypotenuse of this triangle.
Using the Pythagorean theorem, the distance made good can be calculated as:
Distance made good = sqrt((120^2) + (230^2))
= sqrt(14400 + 52900)
= sqrt(67300)
≈ 259.44 nautical miles
To find the True Course, we can use the trigonometric functions sine and cosine. The True Course will be the angle at which the ship is moving relative to the North direction.
Using the tangent function, we can find the angle:
tan(angle) = opposite/adjacent
tan(angle) = 120/230
angle = arctan(120/230)
angle ≈ 27.4°
Since the ship is traveling northwest, the True Course can be calculated by subtracting this angle from 360°:
True Course = 360° - 27.4°
True Course ≈ 332.6°