Case Study Questions on Height and Distance Class 10

Case Study Questions on Height and Distance Class 10

Case Study Questions on Height and Distance Class 10 | Trigonometry Case Studies

Introduction to Class 10 Trigonometry Case Studies

Class 10 mathematics introduces students to practical applications through Case Study Class 10 Trigonometry. These problems connect theory with real-life contexts such as measuring heights of towers, distances between objects, and angles of elevation or depression. By practicing math case study questions class 10 on trigoheight and distance, students gain confidence for board exams.

Importance of Trigonometry Case Studies in Exams

The Case Study Questions Trigonometry Class 10 section helps learners apply sine, cosine, and tangent formulas effectively. Moreover, solving class 10 math height and distance case study questions improves logical reasoning. Therefore, students should practice different problem types for accuracy. Such case studies also strengthen conceptual understanding.

Examples of Height and Distance Applications

Typical case study questions on height and distance class 10 include finding a building’s height from its shadow or calculating the distance of a ship from a lighthouse. Additionally, these Case Study Class 10 Trigonometry examples show how math relates to everyday life. Thus, mastering them is highly beneficial.

Practice Strategy for Success

To excel, focus on NCERT questions, sample papers, and online resources. Since Case Study Questions on Height and Distance Class 10 appear often, consistent practice ensures exam readiness. Finally, review errors carefully and improve step by step.

Case Study 1: Observing a Flagpole from Different Points

Case Study 1

Ritika visits her school ground where a tall flagpole is erected. She wants to calculate the height of the flagpole without actually measuring it directly. She stands at a certain distance from the base of the flagpole and measures the angle of elevation of the top of the pole using a clinometer she made in her science class. She then walks closer to the pole and measures the angle again. Using the two angles of elevation and the distance between the two observation points, she is able to calculate the height of the flagpole. This practical approach shows how trigonometry can be used to find heights of tall objects without physically climbing them. It involves right-angled triangles formed by the line of sight, the height of the flagpole, and the ground.

Formulas used:

\[ \tan\theta = \frac{\text{opposite side}}{\text{adjacent side}}, \]

\[ \sin\theta = \frac{\text{opposite side}}{\text{hypotenuse}}, \quad \cos\theta = \frac{\text{adjacent side}}{\text{hypotenuse}} \]

MCQ Questions

1. Ritika first stands 20 m away from the flagpole and measures the angle of elevation to be 30°. The height of the flagpole is:

  • (a) \(10\sqrt{3}\) m
  • (b) \(20\sqrt{3}\) m
  • (c) 30 m
  • (d) 40 m
Answer: (a) \(10\sqrt{3}\) m
Solution: \(\tan 30^\circ = \dfrac{h}{20} \implies \dfrac{1}{\sqrt{3}} = \dfrac{h}{20} \implies h = \dfrac{20}{\sqrt{3}} = 10\sqrt{3}\).

2. If instead she stands 20 m away and measures angle of elevation as 45°, the height of the flagpole would be:

  • (a) 10 m
  • (b) 15 m
  • (c) 20 m
  • (d) 25 m
Answer: (c) 20 m
Solution: \(\tan 45^\circ = \dfrac{h}{20} \implies 1 = \dfrac{h}{20} \implies h=20\).

3. Ritika then walks 10 m closer to the flagpole. If the angle of elevation now is 60°, what is the height of the pole?

  • (a) \(10\sqrt{3}\) m
  • (b) \(15\sqrt{3}\) m
  • (c) \(20\sqrt{3}\) m
  • (d) \(25\sqrt{3}\) m
Answer: (a) \(10\sqrt{3}\) m
Solution: New distance = 20 – 10 = 10 m.
\(\tan 60^\circ = \dfrac{h}{10} \implies \sqrt{3} = \dfrac{h}{10} \implies h=10\sqrt{3}\).
Correction: Actual answer is (a) \(10\sqrt{3}\) m.

4. Which trigonometric ratio is most useful for solving these height and distance problems?

  • (a) \(\sin\theta\)
  • (b) \(\cos\theta\)
  • (c) \(\tan\theta\)
  • (d) \(\sec\theta\)
Answer: (c) \(\tan\theta\)
Solution: Because \(\tan\theta\) relates vertical height to horizontal distance.

5. If Ritika stands at 15 m from the base and finds the angle of elevation to be \(\arctan(\tfrac{4}{3})\), then the height of the pole is:

  • (a) 15 m
  • (b) 20 m
  • (c) 25 m
  • (d) 30 m
Answer: (b) 20 m
Solution: \(\tan\theta = \dfrac{h}{15} = \tfrac{4}{3} \implies h = \tfrac{4}{3}\times 15 = 20\).
Correction: Correct answer is (b) 20 m.

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