Discussion
The angle of elevation of the top of the tower standing on horizontal plane from point A is α. After walking a distance 'd' towards the foot of the tower, the angle of inclination found to be β. The height of the tower is:
Answer: B
The height is d/ (Cot α - Cot β).
Let the tower have height \(h\) and let \(x\) be the distance from A to its foot. Walking \(d\) towards the tower leaves \(x - d\), where the angle is the larger \(\beta\):
\[ \begin{aligned} x &= h \cot \alpha \\ x - d &= h \cot \beta \\ d &= h(\cot \alpha - \cot \beta) \\ h &= \frac{d}{\cot \alpha - \cot \beta} \end{aligned} \]
The sum \(\cot \alpha + \cot \beta\) applies when the two observation points are on opposite sides of the tower, so that the distances add. The options mixing tan and cot do not come from either case.
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