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Some Applications of Trigonometry
CH09 Question Bank
CBSE_CH09_QUESTION_BANK
Grade 10
Question:
A man standing on the deck of a ship, $8$ m above sea level, observes the angle of elevation of the top of a cliff as $45^\circ$ and the angle of depression of the base of the cliff as $30^\circ$. Find the distance of the cliff from the ship.
Step-by-Step Solution
Key Concept: Use the angle of depression (equal to elevation from the base) to find the horizontal distance directly.
The man's eye level is $8$ m above sea level, and the base of the cliff is at sea level, so the angle of depression to the base gives: $\tan30^\circ=\dfrac{8}{d}$, where $d$ is the horizontal distance. [1.5 Marks]
$\dfrac{1}{\sqrt3}=\dfrac{8}{d}\Rightarrow d=8\sqrt3$ m. [1.5 Marks]
Correct Answer:
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