One-observer height problem
A one-observer height problem is a trigonometry question where one observer, one angle, and one horizontal distance are used to find a height or distance.
Practice This ConceptMain explanation
Teacher explanation
These problems are the standard class 10 application type. One person stands at a known distance from a tower, tree, or pole and measures the angle of elevation or depression. Then one right triangle is formed. The unknown height or horizontal distance is found by choosing the correct ratio, usually tan. The method is simple: sketch, identify sides, write the ratio, and solve.
Example
A student 15 m away from a building sees its top at 45 degrees. Then tan 45 = height/15, so the building height is 15 m.
Simple analogy
One observer means one triangle, one angle, one main ratio.
Common confusion
Students sometimes forget to add the observer's eye height when the question includes it.
Exam tip
Read the question carefully for eye level, ground level, and actual building height. Small wording details change the final answer.
Answer writing and exam use
1-mark use
Write the exact meaning of one-observer height problem in one clean line.
2-mark use
Define one-observer height problem and add one example or condition.
3-mark use
Explain one-observer height problem, show the method or example, and mention the common mistake.
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