Math Case Study Questions Class 10 Trigonometry

Math Case Study Questions Class 10 Trigonometry

CCase Study Questions Trigonometry Class 10

Math Case Study Questions Class 10 Trigonometry

Math 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 3

A tall street light pole stands vertically on the side of a straight road. On a sunny day, the pole casts a shadow on the road. Students of Class 10 decided to calculate the angle of elevation of the Sun by measuring the length of the pole and its shadow. They also verified trigonometric identities using the calculated values of sine, cosine, and tangent. This real-life context connects basic trigonometric ratios to a practical observation. It helps to demonstrate how identities like \(\sin^2\theta + \cos^2\theta = 1\) and \(1 + \tan^2\theta = \sec^2\theta\) can be applied to everyday situations involving right-angled triangles.

1. A pole \(12\) m high casts a shadow of length \(5\) m. The hypotenuse of the right triangle formed is:

  • A) 12 m
  • B) 13 m
  • C) 14 m
  • D) 15 m
Answer: B) 13 m
Solution: Hypotenuse \(= \sqrt{12^2 + 5^2} = \sqrt{144+25} = \sqrt{169} = 13\).

2. The sine of the angle of elevation of the Sun is:

  • A) \(\tfrac{5}{12}\)
  • B) \(\tfrac{12}{13}\)
  • C) \(\tfrac{12}{5}\)
  • D) \(\tfrac{13}{12}\)
Answer: B) \(\tfrac{12}{13}\)
Solution: \(\sin\theta = \dfrac{12}{13}\).

3. The cosine of the angle of elevation of the Sun is:

  • A) \(\tfrac{5}{12}\)
  • B) \(\tfrac{12}{13}\)
  • C) \(\tfrac{5}{13}\)
  • D) \(\tfrac{13}{5}\)
Answer: C) \(\tfrac{5}{13}\)
Solution: \(\cos\theta = \dfrac{5}{13}\).

4. Verify which identity holds for these values of sine and cosine:

  • A) \(\sin^2\theta + \cos^2\theta = 1\)
  • B) \(\sin\theta \cos\theta = 1\)
  • C) \(\tan^2\theta + 1 = \csc^2\theta\)
  • D) \(\cos^2\theta – \sin^2\theta = 1\)
Answer: A) \(\sin^2\theta + \cos^2\theta = 1\)
Solution: \(\left(\tfrac{12}{13}\right)^2 + \left(\tfrac{5}{13}\right)^2 = \tfrac{144}{169} + \tfrac{25}{169} = \tfrac{169}{169} = 1\).

5. If \(\tan\theta = \tfrac{12}{5}\), then \(\sec^2\theta\) equals:

  • A) \(\tfrac{144}{25}\)
  • B) \(\tfrac{169}{25}\)
  • C) \(\tfrac{25}{169}\)
  • D) \(\tfrac{13}{12}\)
Answer: B) \(\tfrac{169}{25}\)
Solution: \(1 + \tan^2\theta = \sec^2\theta\) \(= 1 + \left(\tfrac{12}{5}\right)^2 = 1 + \tfrac{144}{25} = \tfrac{169}{25}\).

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