If a tower subtends angles $\theta$, $2\theta$ and $3\theta$ at three points $A, B$ and $C$ respectively, lying on the same side of a horizontal line through the foot of the tower, $\dfrac{AB}{BC}$ is equal to?

Question

Multiple choice

$\displaystyle \frac{\sin 2 \theta}{\sin \theta} $
$\displaystyle \frac{\sin 3 \theta}{\sin 2 \theta} $
$\displaystyle \frac{\cot \theta - \cot 2 \theta}{\cot 2 \theta- \cot 3 \theta} $

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Accepted Answer

$\displaystyle \frac{\sin 3 \theta}{\sin \theta} $

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