Shadow equals (1/√3) of the height — find the Sun’s elevation angle: The length of the shadow of a vertical tower is 1/√3 times its height. What is the angle of elevation of the Sun?

Introduction / Context:Angle of elevation θ relates height h and shadow s by tan θ = h/s. If s is a fixed fraction of h, tan θ is a fixed constant leading to a standard angle result.

Given Data / Assumptions:

• Shadow length s = (1/√3) × h.
• Vertical tower; level ground.

Concept / Approach:Compute tan θ = h/s = h / (h/√3) = √3, then identify θ from the exact trig value.

Step-by-Step Solution:tan θ = √3 ⇒ θ = 60°

Verification / Alternative check:At 60°, tan = √3; plugging back yields s = h/√3 as stated. The geometry is consistent.

Why Other Options Are Wrong:30° gives tan = 1/√3; 45° gives tan = 1; 90° is vertical and produces no finite shadow; 15° is much smaller.

Common Pitfalls:Using cot instead of tan or misreading “1 √3 times” as √3 times. Here it is explicitly 1/√3 of the height.

Final Answer:60 °