A ship has steamed 230nm N and 180nm W. Find the true course
Make a diagram, you will get a right-angled triangle
use the tangent ratio to find your angle in the triangle
Thank you!
Remember that compass courses, true or magnetic, are clockwise from North, not counterclockwise from East (x axis) as in a math text. This is between 270 (West) and 360 (or zero, North)
To find the true course of a ship, we can use the trigonometric functions and the Pythagorean theorem.
First, let's draw a diagram to represent the ship's movements. The ship steamed 230nm north and 180nm west. Below is a simplified diagram to visualize the ship's direction:
N
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| |
| |
| |
W | |
| |
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To find the true course, we need to calculate the angle between the ship's movement and the true north direction.
1. Use the Pythagorean theorem to find the hypotenuse of the right-angled triangle formed by the ship's movements:
- Hypotenuse^2 = (230nm)^2 + (180nm)^2
- Hypotenuse^2 = 52900nm^2 + 32400nm^2
- Hypotenuse^2 = 85300nm^2
- Hypotenuse ≈ √85300 ≈ 292.19nm
2. Next, we can use trigonometric functions to find the angle (θ) between the ship's movement and the true north direction:
- Cos(θ) = adjacent/hypotenuse
- Sin(θ) = opposite/hypotenuse
- Tan(θ) = opposite/adjacent
Since we want to find the true course, we can use the tangent function:
- Tan(θ) = opposite/adjacent
- Tan(θ) = 230nm / 180nm
- Tan(θ) ≈ 1.2778
Using an inverse tangent function (e.g., arctan, tan^(-1)), we can find the angle θ:
- θ ≈ arctan(1.2778)
- θ ≈ 51.34 degrees
Therefore, the true course of the ship is approximately 51.34 degrees.