Question

If the angles of elevation of the top of a tower from three collinear points $A , B$ and $C$ on a line leading to the foot of the tower are $30^\circ, \, 45^\circ$ and $60^\circ$ respectively, then the ratio $AB : BC$ is

• A. $\sqrt 3 : 1$
• B. $\sqrt 3 : 2$
• C. $1 : \sqrt 3$
• D. $2 : 3$

Answer 1

Answer: (A)

$\sqrt 3 : 1$

Answer 2

$\frac{ AB }{ BC }=\frac{ h (\sqrt{3}-1)}{ h \left(1-\frac{1}{\sqrt{3}}\right)}$
$=\sqrt{3}: 1$