Question

The angles of elevation of the top and foot of a flag staff fixed on a wall are ${60}^o$ and ${45}^o$ to a man, standing on the other end, at a distance of $30$m. Find the height of the flag staff.

• A. $30\sqrt{3}$
• B. $30(\sqrt{3}-1)$m
• C. $30(\sqrt{3}+1)$m
• D. $10\sqrt{3}$m

Answer 1

The correct option is B $30(\sqrt{3}-1)$m

In given figure BC is the height of wall and CD is the height of flag

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

Then in triangle $ABC$

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

$\Rightarrow 1=\frac{BC}{30}$

$\Rightarrow BC=30$

In triangle ABD

$tan{60}^o=\frac{BD}{AB}=\frac{BC+CD}{AB}$

$\Rightarrow \sqrt{3}=\frac{30+CD}{30}$

$\Rightarrow 30\sqrt{3}=30+CD$

$\Rightarrow CD=30\sqrt{3}-30$

$\Rightarrow CD=30(\sqrt{3}-1)$ m