Two-observer distance problem
A two-observer distance problem is a trigonometry question where two viewing positions or two angles are used to find a height or distance.
Practice This ConceptMain explanation
Teacher explanation
In these problems, the object is viewed from two different points or by two observers. The key idea is to make two right triangles that share the same height or object position. Since the height is common, we write two equations and solve them together. These questions often use angles of elevation from two points on the same straight line, such as two positions on the ground or two buildings.
Example
If two students stand at different distances from a tower and see the top at different angles, the tower height can be found by forming two tan equations and solving them.
Simple analogy
Two observers, two triangles, one shared height.
Common confusion
Students may forget that the height is the same in both triangles and write two unrelated equations.
Exam tip
Look for the common height or common horizontal distance first. That shared value is usually the bridge between the two equations.
Answer writing and exam use
1-mark use
Write the exact meaning of two-observer distance problem in one clean line.
2-mark use
Define two-observer distance problem and add one example or condition.
3-mark use
Explain two-observer distance problem, show the method or example, and mention the common mistake.
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