Shadow-based reasoning
Shadow-based reasoning uses the length of a shadow and the angle of elevation of the sun or light source to find a height or distance.
Practice This ConceptMain explanation
Teacher explanation
When sunlight falls on a pole, tree, or building, the object, its shadow, and the sun ray form a right triangle. The shadow becomes the horizontal side, and the height becomes the vertical side. This makes tan the most useful ratio in many shadow questions. These problems are very common because they connect trigonometry with everyday observation.
Example
A tree casts a 12 m shadow when the angle of elevation of the sun is 30 degrees. Then tan 30 = height/12, so the tree height can be found.
Simple analogy
Shadow sits on the ground, so it is the adjacent side.
Common confusion
Students sometimes use the shadow as the slant side instead of the horizontal side.
Exam tip
In shadow questions, always treat the shadow length as the ground side unless the question says the ground is sloping.
Answer writing and exam use
1-mark use
Write the exact meaning of shadow-based reasoning in one clean line.
2-mark use
Define shadow-based reasoning and add one example or condition.
3-mark use
Explain shadow-based reasoning, show the method or example, and mention the common mistake.
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