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Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
Assertion (A): For any acute angle $A$, the value of $\sin A$ can never exceed $1$. Reason (R): In a right triangle, the hypotenuse is always the longest side, so $\dfrac{\text{opposite}}{\text{hypotenuse}}\leq1$.
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: Direct geometric reasoning about right-triangle side lengths.
Since $\sin A=\dfrac{\text{opposite}}{\text{hypotenuse}}$ and the opposite side can never be longer than the hypotenuse, $\sin A\leq1$ always — A is true. [0.5 Mark]
R correctly identifies why: the hypotenuse is the longest side of a right triangle, which is exactly the geometric fact that bounds $\sin A$. [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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