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Some Applications of Trigonometry
CH09 Question Bank
CBSE_CH09_QUESTION_BANK
Grade 10
Question:
From the top of a $75$ m high lighthouse, the angle of depression of a boat is $45^\circ$. Some time later, the boat has moved closer, and the new angle of depression is $60^\circ$. Find the distance the boat travelled.
Step-by-Step Solution
Key Concept: Find the two horizontal distances separately using the two elevation angles (equal to the depression angles), then subtract.
At $45^\circ$: $\tan45^\circ=\dfrac{75}{d_1}\Rightarrow d_1=75$ m. [1.0 Mark]
At $60^\circ$: $\tan60^\circ=\dfrac{75}{d_2}\Rightarrow d_2=\dfrac{75}{\sqrt3}=25\sqrt3$ m. [1.0 Mark]
Distance travelled $=d_1-d_2=75-25\sqrt3=25(3-\sqrt3)$ m $\approx25(3-1.73)=25(1.27)\approx31.75$ m. [1.0 Mark]
Correct Answer:
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