The height of a lighthouse is 100, m. Two boa | vedclass

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(B) Let the height of the lighthouse be $AB = 100\, m$. Let the two boats be at points $C$ and $D$ on opposite sides of the lighthouse.Given that the

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$200\sqrt{3}$

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(B) Let the height of the lighthouse be $AB = 100\, m$. Let the two boats be at points $C$ and $D$ on opposite sides of the lighthouse.Given that the angle of depression from the top $A$ to boats $C$ and $D$ is $30^\circ$,therefore the angle of elevation from $C$ and $D$ to $A$ is also $30^\circ$ (alternate interior angles).In $	riangle ABC$,$	an(30^\circ) = \frac{AB}{BC} \implies \frac{1}{\sqrt{3}} = \frac{100}{BC} \implies BC = 100\sqrt{3}\, m$.In $	riangle ABD$,$	an(30^\circ) = \frac{AB}{BD} \implies \frac{1}{\sqrt{3}} = \frac{100}{BD} \implies BD = 100\sqrt{3}\, m$.The total distance between the two boats is $CD = BC + BD = 100\sqrt{3} + 100\sqrt{3} = 200\sqrt{3}\, m$.Using $\sqrt{3} \approx 1.732$,the distance is $200 	imes 1.732 = 346.4\, m$.

The height of a lighthouse is $100\, m$. Two boats are anchored in the opposite directions from the lighthouse. The angle of depression of each boat from the top of the lighthouse is found to be $30^\circ$. Find the distance between these two boats (in $m$).

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