Question

a ship is 50 miles west and 31 miles south of a harbor what bearing should the captain use to sail directly into the harbor?

Answer 1

To sail into the harbor directly, the captain should use a bearing of approximately 328°, calculated by the arctangent of the opposite over adjacent sides of the right triangle formed by the ship's position and the harbor.

Step-by-step explanation:

To determine the bearing the captain should use to sail directly into the harbor, one can use trigonometric methods. Since the ship is 50 miles west and 31 miles south of the harbor, we can imagine a right triangle where the ship's position and the harbor form the triangle's vertices, with the ship's position at the right angle. The bearing can be found by calculating the angle from the north line rotating clockwise until the line pointing towards the harbor is reached.

First, let's calculate the angle using the arctangent function:

• tan(angle) = opposite/adjacent
• tan(angle) = 50/31
• angle = arctan(50/31)
• angle ≈ 58°

Given that bearing angles are typically measured clockwise from the north, we must adjust this angle because it's from the west. Therefore, the complete bearing is:

• 270° + 58° = 328°

Thus, the captain should use a bearing of 328° to sail directly into the harbor.

Answer 2

31.8 degrees north of east (not sure what format the question wants)

To get this answer you draw a triangle with the line between the ship and the harbor, a line going horizontally, from the ship and ending below the harbor, and a line going vertically down from the harbor to the end of the horizontal line. The horizontal line has a length of 50 and the vertical line has a length of 31. Using inverse tangent, you can find the angle between the ship and the harbor, which is

arctan(opposite/adjacent) opposite being the vertical line, and adjacent being the horizontal line

arctan(31/50) (or tan^-1(31/50))
which gets you 31.8 degrees