Question

An observer standing $50$ m away from a building notices that the angles of elevation of the top and bottom of a flag post on the building are 60${}^o$ and 45${}^o$ respectively. The height of the flag post is _____.

• A. $50$$\sqrt{3}$ m
• B. $50$($\sqrt{3}$ + 1) m
• C. $50$($\sqrt{3}$ - 1) m
• D. $\frac{50}{\sqrt{3}}$

Answer 1

The correct option is C $50$($\sqrt{3}$ - 1) m

Let $AB$ be the tower, $BC$ be the flag post and $D$ be the observer's position.

Then $DA=50$ m, $\angle ADB={45}^o$ and $\angle ADC={60}^o$

Now, tan45${}^o$ = $\frac{AB}{DA}\Rightarrow 1=\frac{AB}{50}\Rightarrow$ AB = 50 m.

And, tan60${}^o$ = $\frac{AC}{OA}\Rightarrow \frac{AC}{50}=\sqrt{3}\Rightarrow \Rightarrow$ AC = 50$\sqrt{3}$ m

$\therefore$ Height of the flag post $=AC-AB$
$=50\sqrt{3}-50$
$=50(\sqrt{3}-1)$m

So, option C is correct.