Similar-triangles under the same Sun — pole and man comparison: A vertical pole 6 m high casts an 8 m shadow. At the same time and place, a man nearby casts a 2.4 m shadow. What is the height of the man (in meters)?

Introduction / Context:When two vertical objects cast shadows at the same time, similar triangles apply: height/shadow is constant. We can scale the man’s shadow by the known ratio from the pole to find the man’s height.

Given Data / Assumptions:

• Pole height = 6 m; its shadow = 8 m
• Man’s shadow = 2.4 m; man’s height = ?
• Same Sun (same solar elevation), level ground.

Concept / Approach:Use height/shadow = constant for both objects (similar right triangles). Thus h_man / 2.4 = 6 / 8.

Step-by-Step Solution:h_man = 2.4 × (6/8) = 2.4 × 0.75 = 1.8 m

Verification / Alternative check:Both give the same tangent ratio: 6/8 = 1.8/2.4 = 0.75, confirming the similarity scaling is correct.

Why Other Options Are Wrong:Values 1.4, 1.6, 2.0, or 1.5 m do not preserve the same height-to-shadow ratio with a 2.4 m shadow.

Common Pitfalls:Inverting the ratio (8/6 instead of 6/8); mixing units (they are already in meters).

Final Answer:1.8 m