Flagstaff shadow — find the Sun’s angle with the ground: A vertical flagstaff of height 6 m casts a shadow of length 2√3 m on level ground. What is the angle of elevation of the Sun (in degrees)?

Introduction / Context:Shadow questions model a right triangle with height as the opposite side and shadow as the adjacent side; thus tan(θ) = height / shadow. Using exact radical values allows a clean angle result.

Given Data / Assumptions:

• Height = 6 m
• Shadow = 2√3 m
• Ground is horizontal; flagstaff is vertical.

Concept / Approach:Compute tan θ and recognize a standard angle whose tangent equals √3.

Step-by-Step Solution:tan θ = 6 / (2√3) = 3 / √3 = √3Therefore, θ = 60° (since tan 60° = √3)

Verification / Alternative check:Using numeric √3 ≈ 1.732, tan θ ≈ 1.732 ⇒ θ ≈ 60°; consistent with standard trigonometric values.

Why Other Options Are Wrong:At 30°, tan = 1/√3; at 45°, tan = 1; at 75°, tan is much larger than √3. “None” is unnecessary since an exact match exists.

Common Pitfalls:Inverting the ratio (shadow/height) and using cot instead of tan; mixing degrees and radians.

Final Answer:60°