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Chapter 9: Applications of Trigonometry

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This page provides comprehensive Chapter 9: Applications of Trigonometry - Assertion Reason Worksheet - SJMaths. Assertion and Reason type questions for Class 10 Applications of Trigonometry. Practice for CBSE Board Exams.

Assertion-Reason Worksheet

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Directions:

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

  • (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.
  1. Question 1:
    Assertion (A): If the angle of elevation of the sun is $30^\circ$, then the shadow of a tower of height $h$ is $h\sqrt{3}$.
    Reason (R): $\tan 30^\circ = \frac{1}{\sqrt{3}}$.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: $\tan 30^\circ = \frac{\text{height}}{\text{shadow}} = \frac{h}{\text{shadow}}$.
    Step 2: $\frac{1}{\sqrt{3}} = \frac{h}{\text{shadow}} \Rightarrow \text{shadow} = h\sqrt{3}$. A is true.
    Step 3: R is the correct value and explains A.
  2. Question 2:
    Assertion (A): The angle of elevation of an object viewed is the angle formed by the line of sight with the horizontal when it is above the horizontal level.
    Reason (R): The angle of depression is formed when the object is below the horizontal level.
    (A)
    (B)
    (C)
    (D)
    Solution: (B)
    Step 1: Both definitions are correct.
    Step 2: R defines depression, which does not explain the definition of elevation in A.
  3. Question 3:
    Assertion (A): If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
    Reason (R): Angle of elevation of the sun is inversely proportional to the length of the shadow.
    (A)
    (B)
    (C)
    (D)
    Solution: (D)
    Step 1: As the sun goes down (angle decreases), the shadow gets longer. So A is false.
    Step 2: R is true (smaller angle $\Rightarrow$ larger cot value $\Rightarrow$ longer shadow).
  4. Question 4:
    Assertion (A): A ladder 14 m long rests against a wall. If the foot of the ladder is 7 m from the wall, then the angle of elevation is $60^\circ$.
    Reason (R): $\cos 60^\circ = \frac{1}{2}$.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: Base = 7, Hypotenuse = 14. $\cos \theta = \frac{7}{14} = \frac{1}{2}$.
    Step 2: $\theta = 60^\circ$. A is true.
    Step 3: R is the correct value used.
  5. Question 5:
    Assertion (A): The angle of depression of a point A on the ground from the top of a tower is $30^\circ$. Then the angle of elevation of the top of the tower from point A is $30^\circ$.
    Reason (R): Angle of elevation and angle of depression are alternate interior angles.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: The horizontal line from the top is parallel to the ground.
    Step 2: The line of sight acts as a transversal, making elevation and depression alternate interior angles.
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