The ratio of the length of a vertical rod to the length of its shadow is 1 : √3. What is the angle of elevation of the Sun?

Introduction / Context:
Shadow problems convert to tan θ = height / shadow. A given ratio directly yields θ by matching to standard angles.

Given Data / Assumptions:

• Height : shadow = 1 : √3 ⇒ height/shadow = 1/√3.

Concept / Approach:
tan θ = height/shadow = 1/√3. Standard angles give tan 30° = 1/√3, so θ = 30°.

Step-by-Step Solution:

Verification / Alternative check:
If θ were 45°, the ratio would be 1 : 1; if 60°, the ratio would be √3 : 1. Neither matches 1 : √3.

Why Other Options Are Wrong:
45° and 60° correspond to different tangent values; 90° would give zero shadow (not this ratio), 15° gives much larger shadow.

Common Pitfalls:
Inverting the ratio; using sine instead of tangent for shadow length.

Final Answer:
30°