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We are given a right triangle with:

- Height of the lighthouse: 175 feet (opposite side).
- Distance of the ship from the base of the lighthouse: 968 feet (adjacent side).
- We need to find the angle of depression \( x \).

To find the angle of depression \( x \), we can use the tangent function:

\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{175}{968}
\]

Now, solve for \( x \) by taking the inverse tangent (arctan):

\[
x = \tan^{-1} \left( \frac{175}{968} \right)
\]

Using a calculator:

\[
x = \tan^{-1} \left( 0.1807 \right) \approx 10.3^\circ
\]

So, the angle of depression \( x \) is approximately **10.3 degrees**.

Would you like more details or have any questions?

Here are five related questions to further your understanding:
1. How would the angle of depression change if the ship moved closer to the lighthouse?
2. What if the lighthouse height increased—how would that affect the angle of depression?
3. Can you calculate the distance offshore if the angle of depression were doubled?
4. How does the tangent function relate to other trigonometric ratios in right triangles?
5. What is the angle of depression when the lighthouse height and the ship’s distance are equal?

**Tip:** When solving for an angle in a right triangle, the inverse of the trigonometric functions (sin, cos, tan) is used to find the angle itself.

Find x, the angle of depression from the top of a lighthouse that is 175 ft above water level to the waterline of a ship 968 ft offshore. Round your answer to the nearest tenth of a degree.

Learn how to calculate the angle of depression from a lighthouse 175 ft above water to a ship 968 ft offshore. This problem covers trigonometry concepts such as the tangent function and inverse tangent, and provides a step-by-step solution. Suitable for high school students.

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