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To solve this problem, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.

### Problem Breakdown:
- Height of the lighthouse's beacon-light (\( h \)): 113 feet
- Angle of elevation (\( \theta \)): 11°
- We need to find the horizontal distance (\( d \)) from the boat to the lighthouse.

### Step-by-Step Solution:
The tangent of the angle of elevation is given by:

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

Plugging in the known values:

\[
\tan(11^\circ) = \frac{113}{d}
\]

Solving for \( d \):

\[
d = \frac{113}{\tan(11^\circ)}
\]

Let's calculate this value.The ship's horizontal distance from the lighthouse is approximately **581.3 feet**.

Would you like more details on the calculation or have any questions? Here are some related questions you might be interested in:

1. How would the distance change if the angle of elevation increased?
2. What if the height of the lighthouse changed? How would that affect the distance?
3. How can we find the vertical distance if the horizontal distance and angle of elevation are known?
4. How does changing the angle affect the accuracy of these measurements in real-world scenarios?
5. What other trigonometric functions can be used for similar problems?

**Tip:** Always make sure your calculator is set to the correct angle mode (degrees or radians) when performing trigonometric calculations.

A boat is heading towards a lighthouse, whose beacon-light is 113 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 11°. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.

Solve a trigonometric problem to find the horizontal distance of a boat from a lighthouse. Using a height of 113 feet and an angle of elevation of 11°, apply the tangent function to calculate the distance. Suitable for high school students learning trigonometry.

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