A vertical pole is 75 m high. What is the angle subtended by the pole at a point on level ground that is 75 m away from its base?

Introduction / Context:
“Angle subtended by the pole” at a ground point is the angle between the lines of sight to the top and bottom of the pole. Since the bottom is at eye level on ground, this reduces to the usual angle of elevation to the top for a vertical object.

Given Data / Assumptions:

• Pole height h = 75 m.
• Horizontal distance x = 75 m.

Concept / Approach:
Angle of elevation θ satisfies tan θ = h / x. With h = x, θ must be 45°.

Step-by-Step Solution:

Verification / Alternative check:
If the point were at 150 m, θ would be arctan(1/2) < 45°; if at 50 m, θ would be arctan(3/2) > 45°—consistent behavior.

Why Other Options Are Wrong:
30° or 60° correspond to x unequal to h; 90° would require zero horizontal distance (impossible for a finite point on the ground).

Common Pitfalls:
Overthinking “subtended angle”; here it equals the elevation angle to the top from level ground.

Final Answer:
45°