As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · July 2023 · Standard
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335 Marks · July 2023 · Standard
As observed from the top of a lighthouse, $100$ m above sea level, the angle of depression of a ship, sailing directly towards it, changes from $30^\circ$ to $45^\circ$. Determine the distance travelled by the ship during the period of observation. (Use $\sqrt{3}= 1.732$)
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Correct figure. In $\triangle ABC$ $\frac{100}{BC} = \tan 45^\circ = 1$ $\Rightarrow BC = 100$ In $\triangle ABD$ $\frac{100}{BD} = \tan 30^\circ = \frac{1}{\sqrt{3}}$ $\Rightarrow BD = 100 \sqrt{3}$ $\Rightarrow 100 + CD = 100 \sqrt{3}$ $\Rightarrow CD = 100 \sqrt{3} - 100 = 100 (1.732 - 1) = 73.2$ Hence, distance travelled by the ship during the period of observation is $73.2$ m
