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Class 10 Maths Chapter 9: Some Applications of Trigonometry Assertion-reason questions with answers

2 assertion-reason questions on Some Applications of Trigonometry, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): If the angle of depression of a boat from the top of a cliff is 30°, then the angle of elevation of the top of the cliff from the boat is also 30°. Reason (R): The angle of depression and the corresponding angle of elevation are alternate angles formed by the line of sight with two parallel horizontal lines.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

The horizontal through the cliff-top is parallel to the sea level, and the line of sight cuts both; alternate angles are equal. So A is true and R is exactly why.

Question 2
Assertion (A): The angle of elevation of the top of a tower is measured from the vertical through the observer's eye. Reason (R): Angles of elevation and of depression are both measured from the horizontal through the observer's eye.
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Answer: (d) A is false, but R is true.

R is the definition and is true. A contradicts it: the angle is measured from the horizontal, not the vertical, so A is false.

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