Question

A person , standing on the bank of a river observer that the angle subtended by tree on the opposite bank is, when he retreats 40 meters from the bank, he finds the angle to be . the height of the tree and the breadth of the river are :

• A. $10\sqrt{3}meters,10meters$
• B. $20\sqrt{3}meters,10meters$
• C. $20\sqrt{3}meters,20meters$
• D. none of these

Answer 1

The correct option is C $20\sqrt{3}meters,20meters$

Here$h$ is height of the tree, and $AB$ be the breath of the river

$A$ be the river position of the man

Now in $△ABC{\tan }^o=\frac{h}{x}=\sqrt{3}$

$h=x\sqrt{3}$

In $△ABC=\tan {30}^o=\frac{h}{40+x}=\frac{1}{\sqrt{3}}$

$=\frac{x\sqrt{3}}{40+x}=\frac{1}{\sqrt{3}}$

$\Rightarrow 3x=40+x$

$\Rightarrow x=20metres$

Height $=x\sqrt{3}=20\sqrt{3}metres$