At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \frac{5}{6}. On walking 70 m towards the tower, the tangent of the angle of elevation of the top of the tower is found to be \frac{9}{8}. What is the height of the tower ?
- A. 225 m ✓
- B. 270 m
- C. 300 m
- D. 330 m
Correct Answer: A. 225 m
Explanation
Let height be h. Initially, \tan A = \frac{h}{x+70} = \frac{5}{6}. After walking 70m, \tan B = \frac{h}{x} = \frac{9}{8}, so x = \frac{8h}{9}. Substituting x into the first equation: \frac{h}{8h/9 + 70} = \frac{5}{6}. Solving this gives 14h = 3150, resulting in h = 225 m.
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