Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is ${45}^{\circ }.$ When he moves $20\text{m}$ away from the bank, he finds the angle of elevation to be ${30}^{\circ }.$ The height of the tree is

• A. $10(\sqrt{3}+1)\text{m}$
• B. $15\sqrt{3}\text{m}$
• C. $20(\sqrt{3}+1)\text{m}$
• D. $10(\sqrt{3}-1)\text{m}$

Answer 1

The correct option is A $10(\sqrt{3}+1)\text{m}$

Let $CD=x$ is the tree and $BC=y$ is the river

From $△BCD,$
$\tan {45}^{\circ }=\frac{x}{y}\Rightarrow 1=\frac{x}{y}\Rightarrow x=y$

Now, from $△ACD,$
$\tan {30}^{\circ }=\frac{x}{20+y}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{x}{20+y}\Rightarrow \sqrt{3}x=20+x(\because x=y)\Rightarrow x=\frac{20}{\sqrt{3}-1}\Rightarrow x=10(\sqrt{3}+1)$

Hence, height of the tree $=10(\sqrt{3}+1)\text{m}$