A man on a cliff observes a boat at an angle of depression of 30° which is approaching the shore to the point…
CBSE Class 10 Maths PYQ · Applications of Trig · Speed Distance · 5 Marks · March 2024 · Standard
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695 Marks · March 2024 · Standard
A man on a cliff observes a boat at an angle of depression of $30^{\circ}$ which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be $60^{\circ}$. Find the time taken by the boat from here to reach the shore.
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Sol. Correct fig. In $\triangle$QAB $\tan60^{\circ} = \sqrt{3} = \frac{h}{x}$ $h=\sqrt{3}x$.........(i) In $\triangle$PAB $\tan30^{\circ} = \frac{h}{y+x} = \frac{1}{\sqrt{3}}$ $y + x=\sqrt{3}h$.........(ii) solving (i) and (ii) $y=2x$ Time taken by the boat from Q to A = $\frac{1}{2} \times 6 =3$ min.
