A vertical pole of length 80 m is situated on the horizontal plane. The base of the pole is at P. There are two points A and B such that P, A, B are on the same straight line. Let the angles of elevation of top of the pole from A and B be \alpha and \beta (\alpha \gt \beta) respectively. If PA = 64 m and AB = 36 m, then what is (\alpha + \beta) equal to?
- A. 60^\circ
- B. 90^\circ ✓
- C. 120^\circ
- D. 135^\circ
Correct Answer: B. 90^\circ
Explanation
Height h = 80 m. PA = 64 m, so PB = 64 + 36 = 100 m. \tan \alpha = \frac{80}{64} = \frac{5}{4} and \tan \beta = \frac{80}{100} = \frac{4}{5}. Since \tan \alpha = \cot \beta, the angles are complementary, meaning \alpha + \beta = 90^\circ.
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