A ship sail 10 nautical miles North then 16 nautical miles west. What is the bearing from its starting point?
It only asked for the bearing, not the distance
tan^-1(16/10) ≈ 57.99 or ≈ 58 degrees , not 56.31 as the bot had
so the bearing is 360-58 ≈ 302 degrees
You're right! I apologize for the error in my previous response. The correct bearing is indeed approximately 302 degrees. Thank you for bringing this to my attention!
To find the bearing from the starting point, we will use trigonometry.
First, let's draw a diagram to visualize the ship's journey. The starting point will be our reference point, at (0,0). The ship sails 10 nautical miles north, so the ship's position will be at (0,10).
Next, the ship sails 16 nautical miles west. Since west is in the negative x-axis direction, the ship's position will be at (-16,10).
We now have a right-angled triangle, where the x-axis represents the horizontal displacement (west) and the y-axis represents the vertical displacement (north).
Using the Pythagorean theorem, we can calculate the hypotenuse of the triangle:
Hypotenuse = √((horizontal displacement)^2 + (vertical displacement)^2)
= √((-16)^2 + (10)^2)
= √(256 + 100)
= √356
≈ 18.87 nautical miles
Now, to find the bearing, we can use trigonometric functions. The bearing is the angle between the x-axis and the line connecting the starting point to the final position of the ship.
To find the angle, we will use the inverse tangent (arctan) function:
Bearing = arctan(vertical displacement / horizontal displacement)
= arctan(10 / -16)
≈ -30.96 degrees
Note that the negative sign indicates rotation in the clockwise direction from the positive x-axis.
Therefore, the bearing from the starting point is approximately 30.96 degrees in the clockwise direction.
To determine the bearing, we need to use trigonometry to find the angle between the ship's starting point and its final position.
First, we can use the Pythagorean theorem to find the distance the ship has traveled from its starting point:
distance = √(10^2 + 16^2) = √356 ≈ 18.87 nautical miles
Next, we can use the inverse tangent function (tan^-1) to find the angle between the ship's starting point and its final position:
angle = tan^-1(16/10) ≈ 56.31°
Finally, we can express the bearing as an angle measured clockwise from due north:
bearing = 360° - 56.31° ≈ 303.69°
Therefore, the ship's bearing from its starting point is approximately 303.69°.