A lighthouse is 9.6 nautical miles from a ship which bears 156 degrees from the lighthouse. How far is the ship east of the lighthouse?

Answer 1

We can use trigonometry and draw a right-angled triangle to solve this problem. Let's label the sides of the triangle:

- The hypotenuse (the side opposite the right angle) is the distance between the ship and the lighthouse, which is 9.6 nautical miles.
- The side opposite the angle of 156 degrees is the distance the ship is south of the lighthouse.
- The side adjacent to the angle of 156 degrees is the distance the ship is east of the lighthouse, which is the value we want to find.

Now we can use trigonometric ratios to find the length of the adjacent side. The appropriate ratio is:

- The cosine of an angle is equal to the adjacent side divided by the hypotenuse.

Therefore, we have:

cos(156 degrees) = adjacent / 9.6

Rearranging this equation to solve for the adjacent side:

adjacent = 9.6 * cos(156 degrees)

Using a calculator, we get:

adjacent = -1.85 nautical miles

The negative value means that the ship is west of the lighthouse, not east. Therefore, we have to add 180 degrees to the angle of 156 degrees to get the angle of the ship's position from the east.

156 degrees + 180 degrees = 336 degrees

Now we can repeat the calculation with this new angle:

cos(336 degrees) = adjacent / 9.6

adjacent = 9.6 * cos(336 degrees)

Using a calculator, we get:

adjacent = 8.25 nautical miles

Therefore, the ship is 8.25 nautical miles east of the lighthouse.

Answer 2

This is the same question as the previous post.
Strangely, the bot got it right in the previous solution, but botched it for this one.
the correct answer is still 3.9 n miles