A 12 cm vertical stick casts an 8 cm shadow at the same time a tower casts a 40 m shadow. Assuming the same sun elevation (similar triangles), find the height of the tower (in metres).

Introduction / Context:When two vertical objects cast shadows simultaneously, the triangles formed by height and shadow length are similar (same sun elevation). Therefore, height is proportional to shadow length; we scale from the stick to the tower.

Given Data / Assumptions:

• Stick height = 12 cm; its shadow = 8 cm.
• Tower shadow = 40 m.
• Both are vertical; ground is level; same sunlight angle (similarity).

Concept / Approach:

• For similar triangles: height/shadow is constant.
• Convert units consistently (use metres).

Step-by-Step Solution:

Verification / Alternative check:Proportion in centimetres also works: 12/8 = H_cm / 4000 ⇒ H_cm = 6000 cm ⇒ 60 m.

Why Other Options Are Wrong:

• 600 m and 160 m: Incorrect scaling or unit mistakes.
• 52 m: Random deviation; not in 3:2 ratio.
• None of these: Not applicable; 60 m is exact.

Common Pitfalls:

• Mismatched units (cm with m) causing wrong scale.
• Assuming non-parallel sun rays; here standard assumption holds.

Final Answer:60 m