C
CraftExam
high importancemedium8 min

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 Concept

Learn the concept

Student-friendly 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.

How to write this in exams

  1. 1

    Start with the exact idea

    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.

  2. 2

    Then show how to use it

    1. Draw the situation. 2. Mark the known distance. 3. Mark the angle. 4. Choose the ratio that connects the known and unknown sides. 5. Solve. 6. Write the answer with units.

  3. 3

    Add one concrete 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.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to use the slant side as the height. The slant side is the line of sight, not the vertical height.

Definition

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.

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.

Rule to remember

For one observer on level ground, tan theta = height / horizontal distance is often the key relation.

Memory hook

One observer means one triangle, one angle, one main ratio.

Examples and method

Worked example

A person stands 12 m from a pole and sees the top at 60 degrees. Using tan 60 = height/12, height = 12 root 3 m.

Method to apply

1. Draw the situation. 2. Mark the known distance. 3. Mark the angle. 4. Choose the ratio that connects the known and unknown sides. 5. Solve. 6. Write the answer with units.

Diagram support

Draw one observer, one object, one right triangle, and label the given angle at the observer or object point as needed.

How CBSE asks it

Find the height of a tree, tower, or pole from one observer, or find the distance of the observer from the object.

Avoid common mistakes

Common confusion

Students sometimes forget to add the observer's eye height when the question includes it.

Common wrong answer

A common wrong answer is to use the slant side as the height. The slant side is the line of sight, not the vertical height.

Exam tip

Read the question carefully for eye level, ground level, and actual building height. Small wording details change the final answer.

Quick check

In a one-observer height problem, what is the first thing you should identify after drawing the sketch?

You should identify the right triangle sides: the known horizontal distance, the unknown height, and the given angle. After that, choose the correct trigonometric ratio, usually tan.

Answer writing and exam use

1-mark answer

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.

2-mark answer

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. For one observer on level ground, tan theta = height / horizontal distance is often the key relation. 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.

3-mark answer

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. For one observer on level ground, tan theta = height / horizontal distance is often the key relation. A person stands 12 m from a pole and sees the top at 60 degrees. Using tan 60 = height/12, height = 12 root 3 m. Find the height of a tree, tower, or pole from one observer, or find the distance of the observer from the object. A common wrong answer is to use the slant side as the height. The slant side is the line of sight, not the vertical height.
MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept