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(B) Let the height of the lighthouse be $h = 60 \ m$ and the distance of the boat from the foot of the lighthouse be $x \ m$.In the right-angled trian

Vedclass · Accepted Answer

$60 \left( \frac{\sqrt{3} + 1}{\sqrt{3} - 1} \right) \ m$

Vedclass · Answer

(B) Let the height of the lighthouse be $h = 60 \ m$ and the distance of the boat from the foot of the lighthouse be $x \ m$.In the right-angled triangle formed by the lighthouse and the sea level,the angle of elevation of the top from the boat is equal to the angle of depression,which is $15^\circ$.Thus,$	an(15^\circ) = \frac{	ext{height}}{	ext{distance}} = \frac{60}{x}$.Therefore,$x = \frac{60}{	an(15^\circ)} = 60 \cot(15^\circ)$.Using the value $\cot(15^\circ) = \frac{\cos(15^\circ)}{\sin(15^\circ)} = \frac{\sqrt{3} + 1}{\sqrt{3} - 1}$.So,$x = 60 \left( \frac{\sqrt{3} + 1}{\sqrt{3} - 1} ight) \ m$.Thus,the correct option is $B$.

From the top of a lighthouse $60 \ m$ high with its base at the sea level,the angle of depression of a boat is $15^\circ$. The distance of the boat from the foot of the lighthouse is:

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