A man standing on the bank of a river observe | vedclass

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(C) Let the tree be represented by $BC$ with height $H$ and the breadth of the river be $DB = x$.From the given figure,in $	riangle DBC$,$	an 60^{\c

Vedclass · Accepted Answer

$18$

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(C) Let the tree be represented by $BC$ with height $H$ and the breadth of the river be $DB = x$.From the given figure,in $	riangle DBC$,$	an 60^{\circ} = \frac{H}{x}$.Since $	an 60^{\circ} = \sqrt{3}$,we have $H = x\sqrt{3} \quad \dots(1)$.In $	riangle ABC$,$	an 30^{\circ} = \frac{H}{AB} = \frac{H}{36 + x}$.Since $	an 30^{\circ} = \frac{1}{\sqrt{3}}$,we have $H = \frac{36 + x}{\sqrt{3}} \quad \dots(2)$.Equating $(1)$ and $(2)$:$x\sqrt{3} = \frac{36 + x}{\sqrt{3}}$$3x = 36 + x$$2x = 36$$x = 18 \ m$.Thus,the breadth of the river is $18 \ m$.

$A$ man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^{\circ}$. When he moves $36 \ m$ away from the bank,he finds the angle to be $30^{\circ}$. Find the breadth of the river (in $m$).

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