Question

The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of $100m$ from its base is ${45}^o$ If the angle of elevation of the top of the complete pillar at the same point is to be ${60}^o$ then the height of the incomplete pillar is to be increased by

• A. $50\sqrt{2}m$
• B. $100m$
• C. $100\left(\sqrt{3-1}\right)m$
• D. $100\left(\sqrt{3+1}\right)m$

Answer 1

The correct option is C $100\left(\sqrt{3-1}\right)m$

Let BC be the incomplete and BD be the complete pillar In Triangles ABC and ABD we have

Given $BC=100$m,

And $\angle CAB={45}^0$$\angle DAB={60}^0$

Let $CD=x$ m

In $\Delta ABC$

$tan{45}^o=\frac{BC}{AB}$

$\Rightarrow 1=\frac{BC}{100}$

$\Rightarrow BC=100m$

In $ABD$

$tan{60}^0=\frac{AD}{AB}$

$\Rightarrow \sqrt{3}=\frac{BD}{100}$

$\Rightarrow BD=100\sqrt{3}$m

Then $BD=BC+CD=100+x$

$\therefore 100+x=100\sqrt{3}$

$\Rightarrow x=100(\sqrt{3}-1)$m