Understanding the Problem
To analyze the situation, we have a building that is 60 m high. From the top of this building, we observe two angles of depression towards the lamp post: one for the top of the lamp post and another for the bottom.
Key Concepts
- Angle of Depression: This is the angle formed between the horizontal line from the observer's eye and the line of sight to an object below the horizontal line.
- Vertical Lamp Post: The lamp post is vertical, meaning it stands straight up from the ground.
Setting Up the Scenario
- The height of the building is 60 m.
- Let the angle of depression to the top of the lamp post be θ1 and to the bottom be θ2.
Using Right Triangles
- Two right triangles are formed:
- The first triangle involves the height of the building and the distance from the base of the building to the base of the lamp post.
- The second triangle involves the height of the lamp post and the same horizontal distance.
Calculating Heights
- The height of the lamp post can be determined using trigonometric ratios:
- For the top of the lamp post: Height = 60 m - (d * tan(θ1))
- For the bottom of the lamp post: Height = 60 m - (d * tan(θ2))
Where 'd' is the horizontal distance from the building to the lamp post.
Conclusion
- By knowing the angles of depression and using trigonometric functions, we can calculate the exact height of the lamp post.
- This problem is a practical application of trigonometry in real-world scenarios, helping to reinforce understanding of angles and heights.