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In the image, we are presented with a trigonometric problem involving a right triangle. Here's a breakdown of the problem:

- There is a lighthouse with a height of 7 meters, and the angle of elevation from a point on the ground to the top of the lighthouse is 12°.
- We need to calculate the horizontal distance from the base of the lighthouse to the point on the ground (denoted by \( x \)).

Using the provided information and basic trigonometric functions:

1. **Given**:
   - Height of the lighthouse: 7 meters (opposite side)
   - Angle of elevation: \( 12^\circ \)
   - Horizontal distance from the base of the lighthouse: \( x \) (adjacent side)

2. **Using the tangent function**:
   \[
   \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{7}{x}
   \]
   where \( \theta = 12^\circ \).

3. **Solving for \( x \)**:
   \[
   x = \frac{7}{\tan(12^\circ)}
   \]

Let me calculate the value of \( x \).The horizontal distance \( x \) from the base of the lighthouse to the point on the ground is approximately 32.93 meters.

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

Here are 5 related questions that build on this problem:
1. What would the horizontal distance be if the angle of elevation were increased to 20°?
2. How would you calculate the total length of the hypotenuse in this triangle?
3. Can you determine the height of the lighthouse if the horizontal distance was 50 meters and the angle of elevation was 15°?
4. How does the value of \( x \) change as the angle of elevation decreases?
5. What trigonometric identity would you use if the hypotenuse was known instead of the opposite side?

**Tip**: When solving problems with right triangles, always ensure you correctly identify the opposite, adjacent, and hypotenuse sides relative to the angle you're working with.

Calculate the horizontal distance from the base of a lighthouse to a point on the ground using trigonometric functions, given a 12° angle of elevation and a 7-meter lighthouse height.

Learn how to solve a trigonometry problem involving a 12° angle of elevation and a 7-meter lighthouse height to calculate the horizontal distance using tangent functions. Suitable for students in Grades 8-10.

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