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Some Applications of Trigonometry
CH09 Question Bank
CBSE_CH09_QUESTION_BANK
Grade 10
Question:
From the top of a cliff $60$ m high, the angle of depression of a boat on the sea is $60^\circ$. The distance of the boat from the base of the cliff is:
$20$ m
$20\sqrt3$ m
$60$ m
$60\sqrt3$ m
$20$ m
$20\sqrt3$ m
$60$ m
$60\sqrt3$ m
Step-by-Step Solution
Key Concept: Apply tanθ = height/distance, using the fact that the angle of depression equals the angle of elevation from the boat.
$\tan60^\circ=\dfrac{60}{d}\Rightarrow \sqrt3=\dfrac{60}{d}$. [0.5 Mark]
$d=\dfrac{60}{\sqrt3}=20\sqrt3$ m. [0.5 Mark]
$d=\dfrac{60}{\sqrt3}=20\sqrt3$ m. [0.5 Mark]
Correct Answer: $20\sqrt3$ m
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