When shadow length equals height, find elevation: If the length of a pole’s shadow on level ground equals the pole’s height, what is the angle of elevation of the light source?

Introduction / Context:Same principle as similar items: tan θ = height/shadow. Equal height and shadow implies tan θ = 1 and θ = 45°.

Given Data / Assumptions:Height = shadow; vertical pole; level ground.

Concept / Approach:Use tan θ = opposite/adjacent.

Step-by-Step Solution:

Verification / Alternative check:A 45°-45°-90° triangle has equal legs, matching the condition.

Why Other Options Are Wrong:30° and 60° correspond to √3 ratios, not equality; 75° would make a very short shadow.

Common Pitfalls:Using sine/cosine instead of tangent; misinterpreting which angle is asked (elevation, not depression).

Final Answer:45°