An observer stands 2 m away from a vertical wall. A light source is placed 6 m away from the same wall, at the same height as the observer. A stick of length 0.5 m, held vertically by the observer at his position, casts a shadow on the wall. What is the width of the shadow on the wall? Round to two decimal places.

Step-by-step solution

1. Identify the similar right‑angled triangles: 1. Triangle formed by the light source, stick top, and the point where the shadow touches the wall. 2. Triangle formed by the stick itself and the part of the wall behind the stick.
2. Compute distances: Distance from light source to stick = 6 m (from wall) - 2 m (from wall) = 4 m. Distance from stick to wall = 2 m.
3. Apply the proportion of similar triangles: \frac{\text{shadow width}}{\text{distance from stick to wall}} = \frac{\text{stick height}}{\text{distance from light source to stick}}. So \frac{W}{2} = \frac{0.5}{4}.
4. Solve for W: \frac{W}{2} = 0.125\;\Rightarrow\; W = 0.25\text{ m}.
5. Round to two decimal places: 0.25 m.

Concept tested: Similar triangles in shadow casting

Published 4 October 2026 · How this solution was prepared and checked