Hello students, we are providing assertion reason questions for class 10. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 10 maths. In this article, you will find assertion reason questions for CBSE Class 10 Maths Chapter 9 Some Applications of Trigonometry. It is a part of Assertion Reason Questions for CBSE Class 10 Maths Series.
| Chapter | Some Applications of Trigonometry |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Some Applications of Trigonometry
Assertion and Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): The height of a tower can be found using only the angle of elevation and the horizontal distance from the base.
Reason $(\mathrm{R})$ : The relation $\tan \theta=\frac{\text { Height }}{\text { Base }}$ holds true in right-angled triangles.
Answer: Option (a) is correct.
Explanation: This is the fundamental method used in trigonometric height-distance problems. Both statements are true and $R$ explains $A$.
Difficulty Level: Moderate
Q2. Assertion (A): If the angle of elevation of the top of a building increases as the observer approaches the building, then the height of the building increases.
Reason (R): A larger angle of elevation implies a taller object.
Answer: Option (d) is correct.
Explanation: The height of the building is fixed. The angle increases as the distance decreases, not because height changes. So A is false and R is also false.
Difficulty Level: Tough
Q3. Assertion (A): When the sun is lower in the sky (early morning or evening), the shadow of a vertical object is longer.
Reason (R): The angle of elevation of the sun is small during early morning or evening.
Answer: Option (a) is correct.
Explanation: A smaller angle of elevation results in a longer shadow (since $\tan \theta=\frac{\text { Height }}{\text { Shadow }}$ ).
Difficulty Level: Conceptual
Q4. Assertion (A): The angle of depression from a lighthouse to a boat is equal to the angle of elevation from the boat to the lighthouse.
Reason (R): These angles are alternate interior angles formed by a transversal intersecting two horizontal lines.
Answer: Option (a) is correct.
Explanation: The horizontal from the eye of the observer at height and the horizontal surface of the water form two parallel lines; line of sight is the transversal.
Difficulty Level: Competency-Based
Q5. Assertion (A): The height of a tower can be calculated by observing the angle of elevation from two different points on a straight line and knowing the distance between them.
Reason (R): Using two angles of elevation and the horizontal distance between observation points, two right triangles can be formed and solved using trigonometric identities.
Answer: Option (a) is correct.
Difficulty Level: Tough
Also check
- Some Applications of Trigonometry Class 10 Assertion Reason Questions Maths Chapter 9
- Introduction to Trigonometry Class 10 Assertion Reason Questions Maths Chapter 8
- Coordinate Geometry Class 10 Assertion Reason Questions Maths Chapter 7
- Triangles Class 10 Assertion Reason Questions Maths Chapter 6
- Arithmetic Progressions Class 10 Assertion Reason Questions Maths Chapter 5
- Quadratic Equations Class 10 Assertion Reason Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Assertion Reason Questions Maths Chapter 3
- Polynomials Class 10 Assertion Reason Questions Maths Chapter 2
- Real Numbers Class 10 Assertion Reason Questions Maths Chapter 1
Topics from which assertion reason questions may be asked
- Heights and Distances
- Line of Sight
- Angle of Elevation and Depression
Trigonometry applications are used in navigation, architecture, and astronomy.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Some Applications of Trigonometry Assertion Reason Questions Class 10
Q1: What does the chapter ‘Some Applications of Trigonometry’ cover?
A1: It builds key concepts related to some applications of trigonometry and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Some Applications of Trigonometry?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from some applications of trigonometry.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
