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

Given data

• Flagstaff: height = 17.5 m, shadow = 40.25 m
• Building: shadow = 28.75 m; find its height

Concept / Approach

• With the same sun elevation, triangles are similar ⇒ height is proportional to shadow length.

Step-by-step calculation

Height / Shadow = constantBuilding height = 17.5 × (28.75 / 40.25)= 17.5 × 0.713422… = 12.5 m

Verification

17.5/40.25 ≈ 0.4348, 12.5/28.75 ≈ 0.4348 (matches).

Common pitfalls

• Using inverse ratio (40.25/28.75) erroneously.

Final Answer

12.5 m