Case Study Questions Class 10 Trigonometry

Case Study Questions Class 10 Trigonometry

Case Study Questions Class 10 Trigonometry with Height and Distance Problems

Case Study Questions Class 10 Trigonometry

Case Study Questions Class 10 Trigonometry plays a vital role in mathematics preparation for board exams. Students encounter practical applications through math case study questions class 10 on trigoheight and distance. These problems help in linking classroom concepts with real-world applications. Moreover, learning through Math Case Study Questions Class 10 enhances logical thinking and accuracy. Therefore, students gain confidence to attempt different exam-oriented problems in a systematic manner.

Importance of Case Study Questions in Trigonometry

Case Study Questions highlight scenarios like buildings, trees, or towers where height and distance are measured. Such class 10 math height and distance case study questions make trigonometry easy and interesting. Additionally, students can practice Case study questions on height and distance class 10 to build problem-solving skills. Importantly, regular practice improves speed and accuracy in exams. As a result, students can strengthen fundamentals effectively.

Case Study 1

A group of architecture students is designing a wheelchair ramp for a public library. According to safety guidelines, the ramp should make a gentle incline with the ground. The students decide to test their design by first building a small model. In the model, the ramp forms a right-angled triangle with the ground and the vertical wall. They measure the base and height of the ramp in their scaled model and then use trigonometric ratios to find the angle of inclination of the ramp. They also verify certain trigonometric identities to check their understanding and ensure accuracy in calculations. This real-life scenario helps in understanding how trigonometric ratios such as sine, cosine, and tangent are related to sides of a right triangle, and how identities connect these ratios.

1. If the height of the ramp is \(3\) m and the base is \(4\) m, then the hypotenuse of the ramp is:

  • A) 4 m
  • B) 5 m
  • C) 6 m
  • D) 7 m
Answer: B) 5 m
Solution: By Pythagoras theorem, hypotenuse \(= \sqrt{3^2+4^2} = \sqrt{9+16} = 5\).

2. The sine of the angle of inclination of the ramp is:

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

3. The cosine of the angle of inclination is:

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

4. Which trigonometric identity is verified using the above values of sine and cosine?

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

5. If \(\tan\theta = \tfrac{3}{4}\) for the ramp’s inclination, then \(\sec^2\theta\) equals:

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

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