From the top of a 300-ft lighthouse, the angle of depression to a ship in the ocean is 23°. How far is the ship from the base of the lighthouse? (Round your answer to the nearest foot.) 

We can solve this problem using trigonometry. The angle of depression from the lighthouse to the ship forms a right triangle, where:

- The height of the lighthouse is 300 feet (opposite side).
- The distance from the base of the lighthouse to the ship is the adjacent side (what we want to find).
- The angle of depression is 23°.

Using the tangent function, which relates the opposite and adjacent sides in a right triangle:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Substituting the known values:

\[
\tan(23^\circ) = \frac{300}{\text{adjacent}}
\]

Now, solve for the adjacent side:

\[
\text{adjacent} = \frac{300}{\tan(23^\circ)}
\]

Let's calculate the value of the adjacent side.The ship is approximately 707 feet away from the base of the lighthouse.

Would you like more details or have any other questions?

Here are 5 related questions to further explore this topic:
1. How would the distance change if the angle of depression was 30° instead of 23°?
2. What if the height of the lighthouse was doubled to 600 feet? How would the distance change?
3. How would you calculate the height of the lighthouse if the distance and angle of depression were known?
4. What is the relationship between the angle of depression and the distance to the ship?
5. How can you use the sine or cosine functions to solve similar problems?

**Tip:** In problems involving angles of depression or elevation, always remember that they are measured relative to a horizontal line, not a vertical line.

From the top of a 300-ft lighthouse, the angle of depression to a ship in the ocean is 23°. How far is the ship from the base of the lighthouse? (Round your answer to the nearest foot.)

Solve a trigonometry problem where the angle of depression from a 300-ft lighthouse to a ship is 23°. Learn how to use the tangent function to find the distance from the base of the lighthouse to the ship, with the answer rounded to the nearest foot.

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