A ship sails 15 nautical miles south then 18 nautical miles west. What is its bearing from its starting point? (to the nearest degree).
Using trigonometry, we can find the angle between the starting point, the southern point, and the final destination as follows:
First, we can draw a right-angled triangle with the starting point at the vertex of the right angle, and the southern and western points as the other two vertices.
Let the angle between the starting point and the southern point be x. Then, using trigonometry:
tan(x) = opposite/adjacent = 15/18
x = tan^-1(15/18) = 41.19 degrees (to 2 decimal places)
Therefore, the bearing of the ship from its starting point is 180 - x = 138.81 degrees (to 2 decimal places), rounded to the nearest degree, which is 139 degrees. Therefore, the ship is bearing 139 degrees from its starting point.
answered has a funny compass.
The ship is WEST of South (180 + something), not East of South
than angle west of south = 18/15 so
180 + tan^-1 ( 1.2 ) = 180 + 50.2 = 230.2
To find the bearing of the ship from its starting point, we can use the concept of trigonometry.
Let's consider the starting point as the origin (0, 0) on a coordinate plane. The ship initially sails 15 nautical miles south, which means it moves 15 units directly downwards on the y-axis, resulting in a new position of (0, -15).
Next, the ship sails 18 nautical miles west, which means it moves 18 units directly to the left on the x-axis from the new position (0, -15). This brings the ship to a new position of (-18, -15).
To find the bearing of the ship from the starting point, we can use the formula:
bearing = arctan(y/x)
Where x and y are the coordinates of the new position relative to the starting point. In this case, x = -18 and y = -15.
Let's substitute these values into the formula and calculate the bearing:
bearing = arctan((-15)/(-18))
≈ arctan(15/18)
≈ arctan(0.8333)
Using a calculator or trigonometry tables, we can find that arctan(0.8333) is approximately 39.47 degrees. Therefore, the bearing of the ship from its starting point is approximately 39.47 degrees to the nearest degree.
To find the bearing from the starting point, we can use trigonometry. The ship sails 15 nautical miles south then 18 nautical miles west, which forms a right triangle. The side opposite to the right angle (the hypotenuse) represents the direct distance from the starting point to the final destination.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse. Let's call it distance "d":
d = √(15^2 + 18^2)
d = √(225 + 324)
d = √549
d ≈ 23.42 nautical miles
To find the bearing, we need to use the inverse tangent function (arctan) to calculate the angle of the triangle. In this case, we'll use the angle between the 18 nautical mile side and the hypotenuse. Let's call this angle "θ":
θ = arctan(18 / 15)
θ = arctan(1.2)
θ ≈ 50.20 degrees
To determine the bearing, we need to identify the compass direction of the angle. In this case, the ship is traveling west (270 degrees) and then south (180 degrees). Adding these two angles to the calculated angle gives us the bearing from the starting point:
Bearing = 270 + 180 + θ
Bearing = 450 + 50.20
Bearing ≈ 500.20 degrees
Therefore, the ship's bearing from its starting point, to the nearest degree, is 500 degrees.