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Some Applications of Trigonometry
CH09 Question Bank
CBSE_CH09_QUESTION_BANK
Grade 10
Question:
Assertion (A): A ladder of length $10$ m makes an angle of $30^\circ$ with the ground; it reaches a height of $5$ m on the wall. Reason (R): Height reached $=\text{ladder length}\times\sin(\text{angle with ground})$.
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: The height on the wall is opposite the ground angle, and the ladder is the hypotenuse.
Height $=10\sin30^\circ=10\times\dfrac12=5$ m — A is true. [0.5 Mark]
R correctly states the formula used (height $=$ ladder length $\times\sin$ of the angle with the ground), which is exactly the method used to verify A — 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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