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To find the angle of depression \( x \) from the top of the lighthouse to the ship, we can use trigonometry. 

The right triangle is formed by:
- The height of the lighthouse (opposite side) = 154 ft.
- The horizontal distance from the lighthouse to the ship (adjacent side) = 1035 ft.
  
We can use the tangent function, which relates the angle to the opposite and adjacent sides:
\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{154}{1035}
\]
Now, solve for \( x \):
\[
x = \tan^{-1}\left(\frac{154}{1035}\right)
\]

First, calculate the ratio:
\[
\frac{154}{1035} \approx 0.1488
\]
Now, take the arctangent of this value:
\[
x = \tan^{-1}(0.1488) \approx 8.5^\circ
\]

Therefore, the angle of depression is approximately **8.5 degrees**.

Would you like further details or have any questions about this solution?

### Related Questions:
1. What is the sine of the angle of depression in this case?
2. How would the angle change if the distance to the ship was reduced by half?
3. Can you find the horizontal distance if the angle of depression was 12° instead?
4. What would happen to the angle of depression if the lighthouse height doubled?
5. How do you calculate the angle of elevation for the same scenario?

### Tip:
Always check whether you are dealing with angles of depression or elevation; the concepts are similar but differ in direction.

Find x, the angle of depression from the top of a lighthouse that is 154 ft above water level to the waterline of a ship 1035 ft off shore. Round your answer to the nearest tenth of a degree.

Learn how to find the angle of depression from a lighthouse to a ship using trigonometric ratios. The problem involves a 154 ft high lighthouse and a ship located 1035 ft off shore. Solve it using the tangent function.

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