Shadow equal to height: When the length of the shadow of a vertical pole equals the height of the pole on level ground, what is the angle of elevation of the light source?

Introduction / Context:
Relating a pole, its shadow, and the angle of elevation uses basic trigonometry: tan θ = opposite/adjacent = height/shadow length.

Given Data / Assumptions:

• Height = shadow length.
• Level ground; vertical pole.

Concept / Approach:
tan θ = height/shadow = 1 → θ = 45°.

Step-by-Step Solution:

Verification / Alternative check:
In a 45°-45°-90° triangle, legs are equal; consistent with the condition.

Why Other Options Are Wrong:
30° or 60° would give unequal legs (shadows √3 h or h/√3), not equal lengths.

Common Pitfalls:
Using sine or cosine instead of tangent; misreading “shadow equals height”.

Final Answer:
45°