A flagstaff 17.5 m high casts a 40.25 m shadow under the sun. Under the same conditions, what is the height of a building that casts a 28.75 m shadow?

Introduction: Height and shadow-length problems under identical sunlight rely on similar triangles: equal solar elevation implies the ratio height/shadow is constant for all vertical objects. We can set up a simple proportion and solve for the unknown building height.

Given Data / Assumptions:

• Flagstaff height = 17.5 m; its shadow = 40.25 m.
• Building shadow = 28.75 m, same sun conditions (same solar angle).
• Let building height be H (in meters).

Concept / Approach: With similar triangles, height/shadow = constant. Hence 17.5/40.25 = H/28.75. Solve for H using cross-multiplication, preserving units in meters for clarity and consistency.

Step-by-Step Solution:

Verification / Alternative check: Compute the common ratio k = height/shadow of the flagstaff = 17.5/40.25 ≈ 0.434. Multiply by 28.75 → 12.5, confirming the proportional result.

Why Other Options Are Wrong: 11.5 m, 12.9 m, 13.2 m, 14.8 m do not preserve the exact ratio; substituting them breaks height/shadow constancy under the same sunlight.

Common Pitfalls: Mixing units or using height/height = shadow/shadow incorrectly. The correct proportion is height/shadow = height/shadow when solar angle is fixed.

Final Answer: 12.5 m