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Some Applications of Trigonometry
CH09 Question Bank
CBSE_CH09_QUESTION_BANK
Grade 10
Question:
Assertion (A): If the angle of elevation of the sun changes from $30^\circ$ to $60^\circ$, the length of a pole's shadow decreases. Reason (R): For a fixed pole height, the shadow length is $h\cot\theta$, and $\cot\theta$ decreases as $\theta$ increases.
Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A. Both Assertion (A) and Reason (R) are true, but R is NOT the correct explanation of A. Assertion (A) is true, but Reason (R) is false. Assertion (A) is false, but Reason (R) is true.
Step-by-Step Solution
Key Concept: As the sun rises higher (larger elevation angle), shadows shrink.
As the elevation angle increases, shadows become shorter (a well-known everyday observation, e.g. shadows are longest at sunrise/sunset and shortest at midday) — A is true. [0.5 Mark]
R correctly gives the formula (shadow $=h\cot\theta$) and correctly notes $\cot\theta$ decreases as $\theta$ increases, which directly explains why the shadow shortens — R correctly explains A. [0.5 Mark]
Correct Answer:Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
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