Question

Then angle of elevation of a top of a tower (point B) from a point A on ground at horizontal distance $d$ from foot of the tower is ${45}^o$. Angle of elevation from a point C $30m$ vertically above point $A$ is ${30}^o$. Then the value of $d$ is

• A. $15(\sqrt{3}+1)$
• B. $15(3+\sqrt{3})$
• C. $30(\sqrt{3}-1)$
• D. $30(3+\sqrt{3})$

Answer 1

Answer: (B)

$15(3+\sqrt{3})$

$\frac{x}{d}=\tan {30}^o;\frac{x}{d}=\frac{1}{\sqrt{3}};d=\sqrt{3}x$
$\frac{x+30}{d}=\tan {45}^o\Rightarrow d=x+30$
$d=\frac{d}{\sqrt{3}}+30\Rightarrow (1-\frac{1}{\sqrt{3}})d=30\Rightarrow d=\frac{30\sqrt{3}}{\sqrt{3}-1}\Rightarrow d=\frac{30\sqrt{3}(\sqrt{3}+1)}{2}=15\sqrt{3}(\sqrt{3}+1)$
$d=15(3+\sqrt{3})$