Assertion and Reason Questions for Class 10 Maths Chapter 9 Applications of Trigonometry PDF

Assertion And Reason Questions For Class 10 Maths Chapter 9 Introduction To Trigonometry are available in this Maths article. Assertion And Reason Questions For Class 10 Maths Chapter 9 Introduction To Trigonometry are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Introduction To Trigonometry. Trigonometry covers ratios like sine, cosine, and tangent, along with identities and angle relationships, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. A free downloadable PDF is also available for easy practice and revision.

Important Assertion And Reason Questions On Some Applications of Trigonometry

Directions: In the following questions a statement of assertion (A) is followed by a statement of reason(R). Mark the correct choice as:

Choose the correct option for the following questions:

• (A). Both Assertion (A) and Reason (R) are true, and Reason is the correct explanation of Assertion.

• (B). Both Assertion (A) and Reason (R) are true, but Reason is not the correct explanation of Assertion.

• (C). Assertion (A) is true, but Reason (R) is false.

• (D). Assertion (A) is false, but Reason (R) is true.

Question 1:

Assertion (A): Trigonometry is used to find heights and distances indirectly.

Reason (R): Direct measurement is sometimes difficult or impossible.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 2:

Assertion (A): The angle formed by looking upward at an object is called the angle of elevation.

Reason (R): The object is above the observer’s eye level.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 3:

Assertion (A): The angle formed by looking downward at an object is called the angle of depression.

Reason (R): The object is below the observer’s eye level.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 4:

Assertion (A): To find the height of a tower, trigonometric ratios can be used.

Reason (R): A right triangle is formed between the observer, the object, and the ground.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 5:

Assertion (A): The ratio used to find height when the base and angle are known is tangent.

Reason (R): Tangent ratio is:tan⁡θ=PerpendicularBase

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 6:

Assertion (A): The height of a building can be calculated using the angle of elevation and horizontal distance.

Reason (R): The building, ground, and line of sight form a right triangle.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 7:

Assertion (A): Angle of elevation is always measured from the horizontal line upward.

Reason (R): The observer looks above the horizontal level.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 8:

Assertion (A): Angle of depression and angle of elevation are equal in many problems.

Reason (R): They are alternate interior angles formed by parallel horizontal lines.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 9:

Assertion (A): If the angle of elevation increases, the height of the object appears greater for the same distance.

Reason (R): The value of tangent increases as the angle increases from (0^\circ) to (90^\circ).

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 10:

Assertion (A): The line joining the observer’s eye and the top of the object is called the line of sight.

Reason (R): The line of sight helps form a right triangle in trigonometric problems.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (B). Both A and R are true, but R is not the correct explanation of A.

Question 11:

Assertion (A): The horizontal distance between the observer and the object forms the base of the right triangle.

Reason (R): The ground is considered horizontal in most trigonometric application problems.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 12:

Assertion (A): To calculate the height of a tree, one may use:tan⁡θ=hd

Reason (R): Here, (h) represents the height and (d) represents the horizontal distance.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 13:

Assertion (A): The observer’s height may need to be added while calculating the total height of an object.

Reason (R): Angles are usually measured from the observer’s eye level.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 14:

Assertion (A): Applications of trigonometry are used in navigation, surveying, and construction.

Reason (R): These fields require indirect measurement of distances and heights.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 15:

Assertion (A): If the distance from the observer to a tower remains fixed, increasing the angle of elevation increases the calculated height.

Reason (R): The value oftan⁡θincreases with increase inθ.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

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