Class 10 Math Height and Distance Case Study Questions

Class 10 Math Height and Distance Case Study Questions

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

Class 10 Math Height and Distance Case Study Questions

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 Class 10 Math Height and Distance Case Study Questions

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 2

Ramesh is a painter who uses a ladder to paint the exterior of a building. The ladder is placed against a wall such that it makes an angle with the ground. The foot of the ladder is at a certain distance from the wall, and the top touches the wall at a certain height. Ramesh wants to make sure that the ladder is safe, so he calculates the angle it makes with the ground using trigonometric ratios. He also checks whether the values satisfy fundamental trigonometric identities. This situation of a ladder forming a right-angled triangle with the wall and ground demonstrates the practical utility of trigonometric ratios and identities in real life. It involves calculating sine, cosine, and tangent of the angle, and verifying their relationships.

1. A ladder \(10\) m long is placed so that the foot is \(6\) m away from the wall. The height at which it touches the wall is:

  • A) 7 m
  • B) 8 m
  • C) 9 m
  • D) 10 m
Answer: B) 8 m
Solution: By Pythagoras theorem, height \(= \sqrt{10^2 – 6^2} = \sqrt{100 – 36} = \sqrt{64} = 8\).

2. The sine of the angle of elevation of the ladder with the ground is:

  • A) \(\tfrac{4}{5}\)
  • B) \(\tfrac{3}{5}\)
  • C) \(\tfrac{3}{4}\)
  • D) \(\tfrac{5}{4}\)
Answer: A) \(\tfrac{4}{5}\)
Solution: \(\sin\theta = \dfrac{8}{10} = \dfrac{4}{5}\).

3. The cosine of the same angle is:

  • A) \(\tfrac{3}{5}\)
  • B) \(\tfrac{4}{5}\)
  • C) \(\tfrac{5}{3}\)
  • D) \(\tfrac{5}{4}\)
Answer: A) \(\tfrac{3}{5}\)
Solution: \(\cos\theta = \dfrac{6}{10} = \dfrac{3}{5}\).

4. Which identity is satisfied by these values of sine and cosine?

  • A) \(\sin^2\theta + \cos^2\theta = 1\)
  • B) \(\sin\theta \cos\theta = \tfrac{1}{2}\)
  • C) \(1 + \tan^2\theta = \csc^2\theta\)
  • D) \(\sin^2\theta – \cos^2\theta = 1\)
Answer: A) \(\sin^2\theta + \cos^2\theta = 1\)
Solution: \(\left(\tfrac{4}{5}\right)^2 + \left(\tfrac{3}{5}\right)^2 = \tfrac{16}{25} + \tfrac{9}{25} = \tfrac{25}{25} = 1\).

5. If \(\tan\theta = \tfrac{4}{3}\), then \(\sec^2\theta\) equals:

  • A) \(\tfrac{16}{9}\)
  • B) \(\tfrac{25}{9}\)
  • C) \(\tfrac{25}{16}\)
  • D) \(\tfrac{9}{25}\)
Answer: B) \(\tfrac{25}{9}\)
Solution: \(1 + \tan^2\theta = \sec^2\theta\) \(1 + \left(\tfrac{4}{3}\right)^2 = 1 + \tfrac{16}{9} = \tfrac{25}{9}\).

Your Results:

Correct Answers: 0

Incorrect Answers: 0

Percentage Score: 0%

Educational Resources Footer

Free Educational Resources

Free Study Material English Vocabulary Tests Grammar for Hearing Impaired Math for Hearing Impaired English Vocabulary Case Study Questions Math GRE Vocabulary Tests LaTeX Tutorial R Programming Tests Online English Games Online Math Games Learn Computer Basics JEE Math Tests CAT Quant Tests Increase Calculation Speed Class 10 Math Tests Prompt Engineering SAT Math Tutorial Logic Quizzes Grade 1 Logic Quizzes Grade 2

© 2023 Udgam Welfare Foundation. All rights reserved.