Geometry

Question Analysis

This question involves Elevation and Depression Angles. The main focus is on leveraging the given distance from the ship to the shore and the angle of elevation to determine the height of the lighthouse. This requires the application of trigonometric principles.

Key Concept Explanation

We rely on the tangent function within a right - triangle context. Here, the horizontal distance from the ship to the shore is the adjacent side of the right - triangle, the height of the lighthouse is the opposite side, and the line of sight from the point on the ship to the top of the lighthouse forms the hypotenuse. The tangent of an angle of elevation is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right - triangle.

Step - by - Step Solution

Let the height of the lighthouse be  meters. The distance from the ship to the shore (adjacent side of the right - triangle),  meters, and the angle of elevation .

We know that .

Since , and , we can set up the equation .

To solve for , we multiply both sides of the equation by 100. So,

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