Which one of the following is <strong>CORRECT</strong>?
Consider the following for the next two (02) items that follow : A flagstaff stands on the top of a vertical tower. The angle of elevation of the top of the flagstaff from a certain place on the same horizontal level with the base of the tower is found to be \alpha. Advancing a distance d towards the tower in the same horizontal plane, the angle of elevation of the top of the flagstaff is observed to be \beta and that of the top of the tower is observed to be \gamma. Let H be the height of the top of the flagstaff from the base of the tower and h be the height of the tower.
- A. d = \frac{H(\cot \alpha - \cot \beta)}{2}
- B. d = \frac{H(\tan \alpha - \tan \beta)}{2}
- C. d = H(\cot \alpha - \cot \beta) ✓
- D. d = H(\tan \alpha - \tan \beta)
Correct Answer: C. d = H(\cot \alpha - \cot \beta)
Explanation
The distance d is the difference in horizontal distances from the flagstaff. From the two positions, the horizontal distances are H \cot \alpha and H \cot \beta. Therefore, d = H \cot \alpha - H \cot \beta = H(\cot \alpha - \cot \beta).
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