The angle of elevation of the top of a lamp post 8 m tall, from a point on the ground is 45o. Find the distance of the point from the foot of the lamp post.

To solve this problem, we can use trigonometry, specifically the tangent function, which relates the angle of elevation, the height of the lamp post, and the distance from the point on the ground to the foot of the lamp post.

Given:
- The height of the lamp post = 8 m
- The angle of elevation = 45°

Let \( d \) represent the distance from the point on the ground to the foot of the lamp post. From the right triangle formed, the tangent of the angle of elevation is given by:

\[
\tan(45^\circ) = \frac{\text{height of the lamp post}}{\text{distance from the foot of the lamp post}}
\]

\[
\tan(45^\circ) = \frac{8}{d}
\]

We know that \( \tan(45^\circ) = 1 \), so:

\[
1 = \frac{8}{d}
\]

Solving for \( d \):

\[
d = 8 \, \text{meters}
\]

Thus, the distance of the point from the foot of the lamp post is **8 meters**.

Would you like a further explanation of the steps? 

Here are five related questions:
1. What is the relationship between the tangent function and angles in a right triangle?
2. How do we solve for distances using trigonometric functions?
3. What is the significance of the angle of elevation in real-world problems?
4. Can you solve a similar problem if the angle of elevation changes?
5. How would the result change if the lamp post was taller?

**Tip:** In trigonometry, special angles like 45°, 30°, and 60° have easily recognizable values for sine, cosine, and tangent, which can simplify calculations.

The angle of elevation of the top of a lamp post 8 m tall, from a point on the ground is 45°. Find the distance of the point from the foot of the lamp post.

Learn how to calculate the distance from a point to the base of a lamp post 8 meters tall using trigonometry. The angle of elevation is 45°, and we use the tangent function to solve this real-world problem. Suitable for Grades 8-10 students.

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