$\"\"$

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The billboard is $\"\"$ wide and is $\"\"$ away from the road.

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Let $\"\"$ be the angle subtended to first end of the billboard.

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From the figure, $\"\"$ .

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Similarly $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, angle subtended by billboard is $\"\"$ . $\"\"$

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To find the maximum angle subtended by billboard, equate $\"\"$ to zero.

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find the maximum angle subtended by billboard by using first derivative test.

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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By the first derivative test, the maximum angle subtended by billboard $\"\"$ .

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$\"\"$

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The point on the road when angle subtended by billboard is maximum is $\"\"$ .